This 2NT shows 22-24 HCP balanced or semi-balanced.

Yes, South can have a five-card major or a six-card minor (often it's better to rebid 2NT when in range with a hand like 

AK2
K9
KQ9542
AK)

Yes, responder can still use Stayman and transfers. Responder, in this case, only needs a couple of points to use Stayman (and 0 points to use transfers, as over 1NT).