The cruise fare will not change with a mid-cruise birthday, as long as he is 2 on embarkation day. If the cruise starts on his birthday, the fare will be for a 3-year-old.
He will only be allowed at the nursery until his actual birthday. On his birthday he will be allowed to attend secured programming in the Club/Lab, as well as any other activities restricted to age 3+ (BBB, maybe some port excursions?). He can continue at the nursery after the birthday if you so choose - many parents prefer it to a newly-turned-3 in with older kids at the Club/Lab. You cannot pre-book anything with the 3+ age limit.