I'm trying to find the best way to do distributed development (2-person team) on Google App Engine.
Are we able to use git or mercurial on GAE?
If not, does that mean we need another server to host our source code (and then deploy from that server)?
Note: I'm a GAE noob.
Since you can develop your application without deploying it to Googles system, you can use any tool and collaboration process you want. This includes a DVCS like git or hg.
If the project that you are developing is going to be open source, you can always host it on Google Code, which will allow you to use Subversion or Mercurial, two excellent, free source control systems.
If it is not open source, you can easily find companies that provide hosted source control solutions, and some of them even have free programs. I can personally recommend Project Locker, which has a free service level for small projects and provides Git and Subversion.
Developing for GAE does not lock you in to any source control system, so use whichever one that you prefer and that is convenient, but kudos to you for thinking yo use it at all. I can't tell you how many times that people of the GAE-related Google Groups inquire about how to get their deployed source code back because they lost their copy of the sourse code.
Yes you should use source control independent from GAE, even with it's deployment versioning.
I've used Unfuddle and Git repositories and it's been very useful, including some simple project management features. It includes a free private plan. Check in all your code to Git then deploy to GAE.