Answers:
1.
Hint:Can you set 2S? 2NT is encouraging. Do you want to encourage? Where is your best likely fit?
Answer. Tthe opponents probably have at least half the deck and eight spades. The chances to set 2S are not good. Passing would be a mistake.
2NT is not a place to bail; it is a game try. This makes sense as notrump contracts are easy to double when the opponents have more points than you do. If the responder as as much as 9 HCP, doubling 2NT is a good bet, and if not, partner will probably have enough to raise to 3NT which could be doubled.
Suit contracts aren't as easy to double at IMPs unless you find somebody with a stack. Your partner has clubs and hearts Is one of these preferable to the other? Partner has at least four of each, and could easily have five clubs that just weren't good enough to overcall at the two level. Partner could have overcalled 1H and didn't, so it's not that likely partner has five hearts. The suggested call is 3C.
2.
Hint: If your partner is minimum for his action, how likely is game?
Answer: This time your hand is better, but with the opponents likely having eight spades between them, passing 2S doubled isn't advisable. You probably only have one spade trick, and may not have any once you leave the double in, implying the spades are in your hand. Your diamond honors are poorly placed.
Now you have enough to try for game with 2NT. Or you could take a shot at 3NT. How will 3NT do if partner is minimum?
While partner shows an opening hand, he is including points for spade (and perhaps diamond) shortness. Partner could have 10 HCP and a singleton spade. Also, when bidding a thin game, it is helpful when the opponents don't know what their best lead is. On this auction, their best lead is very likely spades and you know it. Unless partner has a spade honor, you have one stopper so the opponents will set up three spade tricks in a hurry.
Suits with more than three cards can sometimes produce extra tricks, but neither of your four card suits is going to provide a length trick (unless opener is 4-4-3-2 in which case partner's heart and club suits are breaking badly) and your diamond honors are poorly placed. Your spots are poor. If partner has extra values, you might be able to make 3NT and partner will bid it, but if partner has a minimum double, 2NT is quite enough, and is the recommended bid.
3.
HInt: If your partner is minimum for his action, how likely is game? How well do your hands fit?
Answer: Unlike the last hand, this hand is going to play very well. Partner is short in spades where you have no wastage. All your points are where partner needs them; the C-AQ supporting his four or five card suit, and the DA has to be working. Your nine card heart fit makes your lack of heart honors less relevant.
Consider this:
North has a bare minimum takeout double of 2S and yet
six hearts has play. Partner will have a stronger hand if he has two spades.
North still has a bare minimum, yet you will make 4H unless East has three hearts to the king, unlikely in light of the fact that West opened.
While your job is normally to just pick 3C or 3H here, you have a fantastic hand based on the auction and the recommended action is to jump to 4H.