the template.css file is the one used on the site, you should back it up (which is probably what someone did and that’s why the template_bak.css. You should always backup before you do any changes just in case.
You would have to change the chmod on the files (permissions) to be able to change it.
As far as adding a new module, yes you can do it, just copy the css needed and change it to the new name. If you search the forum you can find good instructions on how to do this. Good luck!
something like:
div.module_new{
padding: 0;
float: left;
clear: both;
width: 100%;
background: #CC0000;