Opening 1NT bids describe a balanced hand in a defined hcp range. Popular choices for 1NT are 12-14 or 15-17 HCP. A problem with using 16-18 for a 1NT opening is that the 1NT rebid to show a balanced minimum hand now shows a very wide range 12-15. Ideally your partnership has an understanding that a minimum rebid in NT always shows at least 12 points and preferably a doubleton in partner's suit
NT rebids are based on the minimum hand shown by partner at that point of the bidding
Do not rescue into NT because you don't like partner's suit. A long weak suit will be a good trump suit, and may offer nothing in a NT contract
16-18hcp was as appropriate range for opening 1NT when a balanced hand with 12 hcp was not considered good enough to open the bidding. Now everyone opens with 12 hcp, 15-17hcp is the recommended range for opening 1NT.
1. Opener rebids 2NT
North has a balanced hand too strong to open 1NT and the 2NT jump rebid is an invitation to bid on to game. It is useful to have a partnership agreement that any bid by responder accepts the game invitation.
2. Opener rebids 2NT over an opponent's overcall
Same as Question 1. The North hand is too strong to open 1NT. With a balanced minimum, North should now pass and rely on South to continue the bidding. With game points South can bid 3H to ask North for a stopper. The overcall does not give North licence to use a 2NT rebid to show a balanced minimum hand.
3. Opener rebids 1NT opposite a passed partner
North is showing a hand too strong to open 1NT (and not strong enough to open 2NT) ie about 19HCP. As a general principle, NT rebids are based on the minimum shown by partner at that point of the auction.
4. East makes a TO Double and rebids 1NT
East's 1NT rebid is based on the minimum values shown by West's response to the TO Double. ie zero hcp. The 1NT rebid shows 18+ hcp, too strong to overcall 1NT.
5. East makes a 1NT overcall and West bids 2H
Is West's 2H bid natural or a transfer to 2S?. You can play it either way but you need to have an agreement with your partner before it happens. Recommended is that continuations are transfers when 1NT overcalls a minor, natural when 1NT overcalls a major.
6. East overcalls 2NT overcall over any Weak 2 opening
Over any weak 2 opening, the 2NT overcall should show a balanced hand of the same range used for your direct 1NT overcall of a 1 level opening. Typically 15-17 or 16-18 hcp. Your partnership should discuss whethe to use Stayman etc and Transfers.