It is possible to create a new foundation that works on a new browser product based on Gecko indeed. You just can't call it Firefox because of trademark ownership.

It would be interesting to see how it collaborates / competes with the origin project, how fast and how far they diverge etc.

You can if you arrange with Foundation to license the trademark under non-profit terms. Not that this is likely to be done by anyone, but if anyone could do it, I’d like to think the Servo group could.