I had mixes, but the most common pet goose is the Sebastopol. I had a Tuffed Roman Emden mix, and she was great. Ganders will be mean during mating season.
My geese ate the Game Bird Crumbles. They don't like pellets. I'd give them the same feed as ducks. I did.
Depends on space and how the geese behave. If you have plenty of space, I don't see why not. If your gander is bad, then most likely not. It really depends on the situation.
If you get the right breed, they'll go broody every year. But as far as hatching.... There's certain feathers you'll need to trim, but I'm not sure which ones. It's for fertilization.
I've raised them together before, and they did really well.