The source code is available in SVN, You can browse the current 810 code online http://svn.linuxmce.org/trac.cgi/browser/branches/LinuxMCE-0810/src
, or you could check it out and view and edit it locally, which you will need to anyway if you're to do any development. There is an article on building 810 in the wiki for more details.
As for developing for 710, imho: let it go! Focus on 810. Your time will be better spent figuring out what prevents 810 from working for you.
1. The xine player specifically is available in http://svn.linuxmce.org/trac.cgi/changeset/22596/branches/LinuxMCE-0810/src/Xine_Player
2. Not really. I'm sure there is some tutorials online, but maybe you should start looking at some code and take it from there. And remember, google is your friend
3. The tickets in trac is both self-assigned, and assigned by others (an admin, for instance).
Well, this is the first oss project I have contributed to also, so my suggestion would be to jump in, like I did. Start off with something you are not quite happy with, investigate it, and make up your mind if it is easy enough for you to do.
As we're in beta now, no new features/functionalities are allowed, but I'm sure there are still some bugs/tweaks to be found..
Oh. btw. there are already some code for VLC intergration in SVN, but it was abandoned for some reason. You should check it out.