YES!!! get them spayed

it really does help with the litter box. when my rabbit became mature, she was peeing everywhere. i got her spayed and it stopped. this was when she was just old enough to be spayed, and now she just turned 4 years old in july! her recovery was fast and she didn't hate me at all. this was a while ago, but from what i remember, the day of, she was kind of sleepy/loopy and next thing i remember, she was back to her old self (the fun kind, not the pee-everywhere kind). soon after we officially bonded, aka, her running on the floor and me ignoring her and she started coming over to me. we are now the best of friends and she loves to snuggle.
just be sure to find a vet who specializes in rabbits. i think one of our MSPCAs does low cost clinics. i got it done at the vet and it was pricey, but so worth it.
as for the above post, i wouldn't say it prevents those things, but maybe tones them down a bit, i have a box in my rabbits cage and if i turn it so it is inclosed with a little door rather than if it turn it so its 3 closed sides and a roof, she might drag hay in an make a nest, hence why i don't turn it that way. she does have her days whats she is a little moody, but it is more than likey because i come home smelling like dogs (grooming) i just have to break out the dried apples and she comes running! same with being picked up. sometimes she will let me and other times she doesn't want to be. she always loves sitting on my lap though. she goes though times where she is digging and chewing in her cardboard box and tube all day long (for entertainment purposes, not nesting) and then other times where she doesn't care. as a whole, she isn't much of a chewer compared to intact rabbits. she behaves well when she is upstairs in my room (she has her own room in the cellar). she is good about going in her litter box in my room, sometimes she goes right outside of it. she will start eating the hay near it and then decide to go right outside rather than hopping in! i have a towel down just in case, so its not a big deal. in her room, her litter box is in her cage and she is 100% litter box trained.