Young rabbits should have alfalfa, but can also have timothy or other grass hay. A mix would be good for them to get used to both kinds and can make it easier when you need to cut the alfalfa. Alfalfa is usually good until they are about 6 months old.
Nursing does could benefit from some alfalfa. Not too much though.
Pregnant does don't really need alfalfa, but a bit probably won't hurt.
You don't want to fatten up rabbits before breeding, so it really wouldn't be a good idea to give alfalfa or other stuff.
Rabbits who are underweight can also have a bit of alfalfa.
Most rabbits other than young ones or nursing does should be fine on timothy or other grass hays. They really don't need to extra calories and such that alfalfa has. You could give a small amount once in a while as a treat.
Breeding rabbits can have some different needs as do those who live outside. However, if they are fed an alfalfa pellet, they should not need alfalfa hay as well.
I don't think it really matters for the nest box, whatever the doe is used to should be fine. You probably don't want to spend a ton, so using what you have is fine. It would probably be better to use something softer, so that may make a difference.
