Those are at the top of the display of file contents. However, they aren't in the tree view, as you've stated. Unfortunately, this is hard because I don't believe Git stores this info in their index of files, which is what is used to generate the tree view. It might be infeasible to gather that data for the tree view.
> Show real dates instead of the vaguely rounded off "how long ago".
If you hover over any relative date, the real date is shown. It's on the title attribute for any relative date.
> Use a readable font on mobile.
The have Consolas and "Liberation Mono" on the font stack, but those probably aren't on your phone. They are limited in font selection because they have switched to native fonts. This avoids the download of some giant font file that contains all the possible glyphs (which is needed on a site like GitHub's). Unfortunately, the monospace options on mobile are pretty limited: http://iosfonts.com/
> Show a directory tree on the left.
Best tip I can offer is to type `t` to search by file name. Works great and has partial matching support, which makes it really quick to navigate to certain key files.