1) What if 2 players wanted to start in the same family but also want characters from different tribes?
The answer is the marriage, you can start a family and your friend join it by marriage (and same gender marriage is allowed).
2) Would one family have to be of the same tribe? Again, since you can join a family by marriage, no matter which tribe they are.
3) How would the offspring be like when the parents are from different tribes? Character appareance depend on their parents, so they will be a mixture of both. In the event that you play one of your children - speculation here - I think you can use the character creator's bars to adjust their appearance. You also have more information about this on this wiki page.
4) Will offspring from people of the same tribe boost tribal bonuses, or marrying people from different tribes possibly cause the offspring to loose a tribal bonus? I am not sure how to answer this, but it is a good question for a Q&A.