You have many questions here, but I'd like to answer the main one:
How do I rename a folder in a GitHub private repo from the git shell
Folders are not tracked directly, but the files within them are tracked based on the pathway. If you have an empty folder that you wish to rename, you would first have to add a file to that folder. It will then be trackable.
I know you mentioned you're on Windows, but I'll show you what this looks like on OS X:
bash-3.2$ ls
archetypes config.yaml data public
config.toml content posts themes
bash-3.2$ git status
On branch master
nothing to commit, working directory clean
bash-3.2$ ls posts/
404.html page
apple-touch-icon-144-precomposed.png page.html
css posts
favicon.png posts.html
index.html sitemap.xml
index.xml touch-icon-144-precomposed.png
js
bash-3.2$ mv posts/ posts_other/
bash-3.2$ ls
archetypes config.yaml data public
config.toml content posts_other themes
bash-3.2$ git status
On branch master
Changes not staged for commit:
deleted: posts/.html
deleted: posts/404.html
deleted: posts/apple-touch-icon-144-precomposed.png
deleted: posts/css/highlight/arta.css
deleted: posts/css/highlight/ascetic.css
deleted: posts/css/highlight/atelier-dune.dark.css
deleted: posts/css/highlight/atelier-dune.light.css
deleted: posts/css/highlight/atelier-forest.dark.css
deleted: posts/css/highlight/atelier-forest.light.css
deleted: posts/css/highlight/atelier-heath.dark.css
deleted: posts/css/highlight/atelier-heath.light.css
deleted: posts/css/highlight/atelier-lakeside.dark.css
deleted: posts/css/highlight/atelier-lakeside.light.css
deleted: posts/css/highlight/atelier-seaside.dark.css
deleted: posts/css/highlight/atelier-seaside.light.css
deleted: posts/css/highlight/codepen-embed.css
deleted: posts/css/highlight/color-brewer.css
deleted: posts/css/highlight/dark.css
deleted: posts/css/highlight/default.css
deleted: posts/css/highlight/docco.css
deleted: posts/css/highlight/far.css
deleted: posts/css/highlight/foundation.css
deleted: posts/css/highlight/github.css
deleted: posts/css/highlight/googlecode.css
deleted: posts/css/highlight/hybrid.css
deleted: posts/css/highlight/idea.css
deleted: posts/css/highlight/ir_black.css
deleted: posts/css/highlight/kimbie.dark.css
deleted: posts/css/highlight/kimbie.light.css
deleted: posts/css/highlight/magula.css
deleted: posts/css/highlight/mono-blue.css
deleted: posts/css/highlight/monokai.css
deleted: posts/css/highlight/monokai_sublime.css
deleted: posts/css/highlight/obsidian.css
deleted: posts/css/highlight/paraiso.dark.css
deleted: posts/css/highlight/paraiso.light.css
deleted: posts/css/highlight/railscasts.css
deleted: posts/css/highlight/rainbow.css
deleted: posts/css/highlight/solarized_dark.css
deleted: posts/css/highlight/solarized_light.css
deleted: posts/css/highlight/sunburst.css
deleted: posts/css/highlight/tomorrow-night-blue.css
deleted: posts/css/highlight/tomorrow-night-bright.css
deleted: posts/css/highlight/tomorrow-night-eighties.css
deleted: posts/css/highlight/tomorrow-night.css
deleted: posts/css/highlight/tomorrow.css
deleted: posts/css/highlight/vs.css
deleted: posts/css/highlight/xcode.css
deleted: posts/css/highlight/zenburn.css
deleted: posts/css/hyde-overrides.css
deleted: posts/css/hyde-x.css
deleted: posts/css/hyde.css
deleted: posts/css/poole-overrides.css
deleted: posts/css/poole.css
deleted: posts/css/syntax.css
deleted: posts/favicon.png
deleted: posts/index.html
deleted: posts/index.xml
deleted: posts/js/highlight.pack.js
deleted: posts/page.html
deleted: posts/page/1.html
deleted: posts/posts.html
deleted: posts/posts/first.html
deleted: posts/posts/first/index.html
deleted: posts/posts/index.html
deleted: posts/posts/index.xml
deleted: posts/sitemap.xml
deleted: posts/touch-icon-144-precomposed.png
Untracked files:
posts_other/
no changes added to commit
bash-3.2$ git add posts_other/
bash-3.2$ git status
On branch master
Changes to be committed:
new file: posts_other/.html
new file: posts_other/404.html
new file: posts_other/apple-touch-icon-144-precomposed.png
new file: posts_other/css/highlight/arta.css
new file: posts_other/css/highlight/ascetic.css
new file: posts_other/css/highlight/atelier-dune.dark.css
new file: posts_other/css/highlight/atelier-dune.light.css
new file: posts_other/css/highlight/atelier-forest.dark.css
new file: posts_other/css/highlight/atelier-forest.light.css
new file: posts_other/css/highlight/atelier-heath.dark.css
new file: posts_other/css/highlight/atelier-heath.light.css
new file: posts_other/css/highlight/atelier-lakeside.dark.css
new file: posts_other/css/highlight/atelier-lakeside.light.css
new file: posts_other/css/highlight/atelier-seaside.dark.css
new file: posts_other/css/highlight/atelier-seaside.light.css
new file: posts_other/css/highlight/codepen-embed.css
new file: posts_other/css/highlight/color-brewer.css
new file: posts_other/css/highlight/dark.css
new file: posts_other/css/highlight/default.css
new file: posts_other/css/highlight/docco.css
new file: posts_other/css/highlight/far.css
new file: posts_other/css/highlight/foundation.css
new file: posts_other/css/highlight/github.css
new file: posts_other/css/highlight/googlecode.css
new file: posts_other/css/highlight/hybrid.css
new file: posts_other/css/highlight/idea.css
new file: posts_other/css/highlight/ir_black.css
new file: posts_other/css/highlight/kimbie.dark.css
new file: posts_other/css/highlight/kimbie.light.css
new file: posts_other/css/highlight/magula.css
new file: posts_other/css/highlight/mono-blue.css
new file: posts_other/css/highlight/monokai.css
new file: posts_other/css/highlight/monokai_sublime.css
new file: posts_other/css/highlight/obsidian.css
new file: posts_other/css/highlight/paraiso.dark.css
new file: posts_other/css/highlight/paraiso.light.css
new file: posts_other/css/highlight/railscasts.css
new file: posts_other/css/highlight/rainbow.css
new file: posts_other/css/highlight/solarized_dark.css
new file: posts_other/css/highlight/solarized_light.css
new file: posts_other/css/highlight/sunburst.css
new file: posts_other/css/highlight/tomorrow-night-blue.css
new file: posts_other/css/highlight/tomorrow-night-bright.css
new file: posts_other/css/highlight/tomorrow-night-eighties.css
new file: posts_other/css/highlight/tomorrow-night.css
new file: posts_other/css/highlight/tomorrow.css
new file: posts_other/css/highlight/vs.css
new file: posts_other/css/highlight/xcode.css
new file: posts_other/css/highlight/zenburn.css
new file: posts_other/css/hyde-overrides.css
new file: posts_other/css/hyde-x.css
new file: posts_other/css/hyde.css
new file: posts_other/css/poole-overrides.css
new file: posts_other/css/poole.css
new file: posts_other/css/syntax.css
new file: posts_other/favicon.png
new file: posts_other/index.html
new file: posts_other/index.xml
new file: posts_other/js/highlight.pack.js
new file: posts_other/page.html
new file: posts_other/page/1.html
new file: posts_other/posts.html
new file: posts_other/posts/first.html
new file: posts_other/posts/first/index.html
new file: posts_other/posts/index.html
new file: posts_other/posts/index.xml
new file: posts_other/sitemap.xml
new file: posts_other/touch-icon-144-precomposed.png
Changes not staged for commit:
deleted: posts/.html
deleted: posts/404.html
deleted: posts/apple-touch-icon-144-precomposed.png
deleted: posts/css/highlight/arta.css
deleted: posts/css/highlight/ascetic.css
deleted: posts/css/highlight/atelier-dune.dark.css
deleted: posts/css/highlight/atelier-dune.light.css
deleted: posts/css/highlight/atelier-forest.dark.css
deleted: posts/css/highlight/atelier-forest.light.css
deleted: posts/css/highlight/atelier-heath.dark.css
deleted: posts/css/highlight/atelier-heath.light.css
deleted: posts/css/highlight/atelier-lakeside.dark.css
deleted: posts/css/highlight/atelier-lakeside.light.css
deleted: posts/css/highlight/atelier-seaside.dark.css
deleted: posts/css/highlight/atelier-seaside.light.css
deleted: posts/css/highlight/codepen-embed.css
deleted: posts/css/highlight/color-brewer.css
deleted: posts/css/highlight/dark.css
deleted: posts/css/highlight/default.css
deleted: posts/css/highlight/docco.css
deleted: posts/css/highlight/far.css
deleted: posts/css/highlight/foundation.css
deleted: posts/css/highlight/github.css
deleted: posts/css/highlight/googlecode.css
deleted: posts/css/highlight/hybrid.css
deleted: posts/css/highlight/idea.css
deleted: posts/css/highlight/ir_black.css
deleted: posts/css/highlight/kimbie.dark.css
deleted: posts/css/highlight/kimbie.light.css
deleted: posts/css/highlight/magula.css
deleted: posts/css/highlight/mono-blue.css
deleted: posts/css/highlight/monokai.css
deleted: posts/css/highlight/monokai_sublime.css
deleted: posts/css/highlight/obsidian.css
deleted: posts/css/highlight/paraiso.dark.css
deleted: posts/css/highlight/paraiso.light.css
deleted: posts/css/highlight/railscasts.css
deleted: posts/css/highlight/rainbow.css
deleted: posts/css/highlight/solarized_dark.css
deleted: posts/css/highlight/solarized_light.css
deleted: posts/css/highlight/sunburst.css
deleted: posts/css/highlight/tomorrow-night-blue.css
deleted: posts/css/highlight/tomorrow-night-bright.css
deleted: posts/css/highlight/tomorrow-night-eighties.css
deleted: posts/css/highlight/tomorrow-night.css
deleted: posts/css/highlight/tomorrow.css
deleted: posts/css/highlight/vs.css
deleted: posts/css/highlight/xcode.css
deleted: posts/css/highlight/zenburn.css
deleted: posts/css/hyde-overrides.css
deleted: posts/css/hyde-x.css
deleted: posts/css/hyde.css
deleted: posts/css/poole-overrides.css
deleted: posts/css/poole.css
deleted: posts/css/syntax.css
deleted: posts/favicon.png
deleted: posts/index.html
deleted: posts/index.xml
deleted: posts/js/highlight.pack.js
deleted: posts/page.html
deleted: posts/page/1.html
deleted: posts/posts.html
deleted: posts/posts/first.html
deleted: posts/posts/first/index.html
deleted: posts/posts/index.html
deleted: posts/posts/index.xml
deleted: posts/sitemap.xml
deleted: posts/touch-icon-144-precomposed.png
bash-3.2$ git add .
bash-3.2$ git commit -m "Renamed post repository to posts_other"
[master 073ed6250b97] Renamed post repository to posts_other
68 files changed, 0 insertions(+), 0 deletions(-)
rename {posts => posts_other}/.html (100%)
rename {posts => posts_other}/404.html (100%)
rename {posts => posts_other}/apple-touch-icon-144-precomposed.png (100%)
rename {posts => posts_other}/css/highlight/arta.css (100%)
rename {posts => posts_other}/css/highlight/ascetic.css (100%)
rename {posts => posts_other}/css/highlight/atelier-dune.dark.css (100%)
rename {posts => posts_other}/css/highlight/atelier-dune.light.css (100%)
rename {posts => posts_other}/css/highlight/atelier-forest.dark.css (100%)
rename {posts => posts_other}/css/highlight/atelier-forest.light.css (100%)
rename {posts => posts_other}/css/highlight/atelier-heath.dark.css (100%)
rename {posts => posts_other}/css/highlight/atelier-heath.light.css (100%)
rename {posts => posts_other}/css/highlight/atelier-lakeside.dark.css (100%)
rename {posts => posts_other}/css/highlight/atelier-lakeside.light.css (100%)
rename {posts => posts_other}/css/highlight/atelier-seaside.dark.css (100%)
rename {posts => posts_other}/css/highlight/atelier-seaside.light.css (100%)
rename {posts => posts_other}/css/highlight/codepen-embed.css (100%)
rename {posts => posts_other}/css/highlight/color-brewer.css (100%)
rename {posts => posts_other}/css/highlight/dark.css (100%)
rename {posts => posts_other}/css/highlight/default.css (100%)
rename {posts => posts_other}/css/highlight/docco.css (100%)
rename {posts => posts_other}/css/highlight/far.css (100%)
rename {posts => posts_other}/css/highlight/foundation.css (100%)
rename {posts => posts_other}/css/highlight/github.css (100%)
rename {posts => posts_other}/css/highlight/googlecode.css (100%)
rename {posts => posts_other}/css/highlight/hybrid.css (100%)
rename {posts => posts_other}/css/highlight/idea.css (100%)
rename {posts => posts_other}/css/highlight/ir_black.css (100%)
rename {posts => posts_other}/css/highlight/kimbie.dark.css (100%)
rename {posts => posts_other}/css/highlight/kimbie.light.css (100%)
rename {posts => posts_other}/css/highlight/magula.css (100%)
rename {posts => posts_other}/css/highlight/mono-blue.css (100%)
rename {posts => posts_other}/css/highlight/monokai.css (100%)
rename {posts => posts_other}/css/highlight/monokai_sublime.css (100%)
rename {posts => posts_other}/css/highlight/obsidian.css (100%)
rename {posts => posts_other}/css/highlight/paraiso.dark.css (100%)
rename {posts => posts_other}/css/highlight/paraiso.light.css (100%)
rename {posts => posts_other}/css/highlight/railscasts.css (100%)
rename {posts => posts_other}/css/highlight/rainbow.css (100%)
rename {posts => posts_other}/css/highlight/solarized_dark.css (100%)
rename {posts => posts_other}/css/highlight/solarized_light.css (100%)
rename {posts => posts_other}/css/highlight/sunburst.css (100%)
rename {posts => posts_other}/css/highlight/tomorrow-night-blue.css (100%)
rename {posts => posts_other}/css/highlight/tomorrow-night-bright.css (100%)
rename {posts => posts_other}/css/highlight/tomorrow-night-eighties.css (100%)
rename {posts => posts_other}/css/highlight/tomorrow-night.css (100%)
rename {posts => posts_other}/css/highlight/tomorrow.css (100%)
rename {posts => posts_other}/css/highlight/vs.css (100%)
rename {posts => posts_other}/css/highlight/xcode.css (100%)
rename {posts => posts_other}/css/highlight/zenburn.css (100%)
rename {posts => posts_other}/css/hyde-overrides.css (100%)
rename {posts => posts_other}/css/hyde-x.css (100%)
rename {posts => posts_other}/css/hyde.css (100%)
rename {posts => posts_other}/css/poole-overrides.css (100%)
rename {posts => posts_other}/css/poole.css (100%)
rename {posts => posts_other}/css/syntax.css (100%)
rename {posts => posts_other}/favicon.png (100%)
rename {posts => posts_other}/index.html (100%)
rename {posts => posts_other}/index.xml (100%)
rename {posts => posts_other}/js/highlight.pack.js (100%)
rename {posts => posts_other}/page.html (100%)
rename {posts => posts_other}/page/1.html (100%)
rename {posts => posts_other}/posts.html (100%)
rename {posts => posts_other}/posts/first.html (100%)
rename {posts => posts_other}/posts/first/index.html (100%)
rename {posts => posts_other}/posts/index.html (100%)
rename {posts => posts_other}/posts/index.xml (100%)
rename {posts => posts_other}/sitemap.xml (100%)
rename {posts => posts_other}/touch-icon-144-precomposed.png (100%)
bash-3.2$
In regards to your problems sharing code between Windows & Linux, there are very good tutorials on the matter. Here is what I used and I also refer to this blog.
Most importantly, make sure to set your text attributes wisely as this other question answers (because CRLF is a jerk).
