[Knurdler]

A new partner has got me learning 2 way checkback (TWCB) and my job is to draft a simple agreement.
Do I need to say we play SAYC and Walsh style?
My questions are only on invitational sequences.

After 1m 1S 1NT 2C 2D, I am comfortable with responders third bids of: pass= to play in D; 2H = 4H (and hence 5s); 2S = 5S (denies 4H).
With 4H and 4H, responder would have started with 1H. What does 2NT show?

After 1m 1H 1NT 2C 2D, I am not so sure. Pass = to play in D; 2H = 5H and denies 4S seems reasonable. But is 2S = 4/4 or 5/4? What is 2NT?

Thanks