The command cd "'$f/'" contains outer double-quotes that will be removed by the shell after they serve they purpose of quoting. The inner single-quotes will survive and get to cd as parts of the argument. (More about quotes within quotes here: Parameter expansion (variable expansion) and quotes within quotes.)
In effect you're trying to cd to e.g. 'Folder 1/' with literal single-quotes, while the existing target is Folder 1/. There is no 'Folder 1/' directory.
Additionally * matches non-directories as well. a.sh is the script. After you add / and single-quotes, you're trying to cd to 'a.sh/'. There is no such directory.
Having failed to cd into this non-directoriy, you then subsequently also run cd .., which will take you out of the starting directory, and into its parent. From here, the entities that the original * matched are no longer visible, and so all further attempts to cd fail too... in fact, each subsequent failed cd will take you up one directory.
You need for f in */ to iterate over directories only (but note * doesn't match dotfiles). Then you don't need to add / because the trailing slash appears from the expansion of $f (although another trailing slash shouldn't break anything). And you absolutely shouldn't add single-quotes to the argument of cd. The relevant line should be cd "$f".
You could use a loop like the following to iterate through all entities, skipping non-directories, and handling cd errors correctly:
[ ! -d "${f}" ] && continue to skip non-directories (note: this will still match symlinks that point at directories)cd "${f}" || continue to skip directories we can't enter (e.g: permissions)pushd "${f}" / popd to avoid relative cd return attempts
for f in *; do
# skip non-directories
[ ! -d "$f" ] && continue
# skip processing for directories we can't enter (e.g: permissions)
pushd "$f" || continue
echo "hi"
pwd
popd
done
