1. I would bring her to a vet, a good rabbit vet, and have him palpate her or use whatever method he finds best, to find out if she is pregnant or not and then go from there. I would have her spayed because:
A)She's too young. B)The doe and buck are brother and sister which can cause alot of problems and could end up costing you alot of money in vets bills and you wouldn't be able to rehome the babies. C) I don't think you are able to care for the mother and babies.
2. In total you need three hutches. One hutch for the mother. One hutch for the father. One hutch for the babies when they are being weaned off the mother.
3.Sorry I don't understand three.
4. The fact that she is such a young doe increases the chance of her having complications in birth such as stuck kittens etc. As someone here once described it, breeding a doe that young is like a 13 year old having a baby. I do highly recommend you and your mother take your doe to the vets and see if she's pregnant. There is a high chance she is not pregnant. He might not be mature enough to get her pregnant, she might not be mature enough to get pregnant, or a combination of both.
Just to add, the way I see it is, the cost of the trip to the vet and the spay could cost alot less then the bills for the kits who could have alot wrong with them, teeth problems etc. The cost to buy hutches for EVERY baby and the cost to feed them, because yes, if they have health problems you cannot give them away and the chances are no one would take them anyway.
At the end of the day, their your rabbits so you and your family need to do what you think is best for all of ye and the rabbits, good luck!