Couple things:
1. A lot of your files are size 0, which means they have nothing in them.
2. A .zip is a compressed archive of a bunch of files, unless you unzip it you will not be able to do anything with it.
If your .zip contains the entire website, I recommend deleting
everything in public_html (just to make sure uploading your site won't put you over quota again), unzipping your .zip file, and then uploading the contents of that.
Also, do you mind telling us a brief overview of what your site's purpose is? I'm seeing a lot of random stuff on there and I can't quite piece together whether or not your site would actually be allowed here should you finish it. For reference, a list of what we do/do not allow is at
http://x10hosting.com/terms and
http://x10hosting.com/aup