gnuplot has a set of commands and a set of options for each command. The name of each command and option can be abbreviated to the shortest unique string that describes it, e.g. p for the plot command, sp for the splot command, t for the title option to plot. Note that you can't, for example, use s for splot because it conflicts with set.
The two-letter abbreviations in gnuplot starting with l are usually for a line characteristic, like lt for linetype, lw for linewidth. These are actually unique flags which can be used interchangeably with the long form: lw, linew and linewidth specify the same option. You can see this in the command-line documentation for the set style line command:
help set style line
This gives
Syntax:
set style line <index> default
set style line <index> {{linetype | lt} <line_type> | <colorspec>}
{{linecolor | lc} <colorspec>}
{{linewidth | lw} <line_width>}
{{pointtype | pt} <point_type>}
{{pointsize | ps} <point_size>}
{{pointinterval | pi} <interval>}
{palette}
unset style line
show style line
and you can see that the options separated by a pipe ('|') are equivalent.
To be safe when starting with gnuplot, I recommend typing out the full commands, and when you get more experienced/lazy you can start abbreviating more.
[EDIT] to finish answering your questions:
1) lt stands for linetype. You can see what the line types are for the current terminal with the test command.
2) noti stands for notitle, which does what you think.
3) The last two lines draw f(1-g(x)) with no title and a 0.75pt wide red line; and f(12.5*g(x)) with no title and a 0.75pt gray line.
