There is laws about protecting trademarks and one needs to apply for a one to protect it. Even then there is lot of court cases when someone tries exploit a well known trademark. So currently the name F12 is free game.

The domains are not controlled in any way, only if there is a trademark holder who wishes to enforce it's rights later then usually court case is needed or parties must make agreement. And in this case domains were granted before trademark was so even if RG wouldn't have trademark there would be a good case to keep the domains still because they were given before the trademark was applied.

With all legal this legal censored and my experience with open source software projects (we could see a common relation to this case) I would be really careful unless this is going to be one man project that is called F12. If others participate there must be a good license for ensuring that contributors get their share of control etc, otherwise there will be other competing projects.

I just wanted to point out that these must be considered when creating a license and everyone in the class needs to have their say. Also for creating a commercially viable product trademarks and such must be considered (maybe too early for that?).