Answers: (Material in blue may be too advanced for some novices.)
1.
Hint: To your knowledge, what is your best fit?
Answer: Your partner has shown at least five spades and at least four hearts. It is unlikely that partner has more hearts than spades, but quite likely that partner has more spades than hearts. Bid 2S. You might ask, "Won't partner think I have something if I bid?" You already passed 1S; you have less than six points. Partner won't think you found a hidden ace, they will assume that you think spades is a better trump suit than hearts.
Some might have wanted to bid 2NT. First, even if you score a club trick, partner will need to promote spades and/or hearts and that will give the opponents time to take their clubs.
You virtually never bid 2NT just to play in a competitive situation. If it turns out that the opponents have more strength than your side, 2NT is quite easy to double.
2.
Hint: What does partner have?
Answer: You might think that partner can have no more than 21 points and you have 2 (4 if you count your doubletons) so why would one think about anything but playing 2H?
However, you have a great-fitting hand for partner. The queen in partner's spade suit rates to be very helpful. Think of this, sometimes partner is going to be 5-5. Give partner as little as AKxxx in each major, and ten tricks are going to be easy. Partner could easily have more; and some 5-4's have excellent play for 4H.
Consider that your right hand opponent didn't raise clubs, that means that partner is more likely to have three clubs which makes your doubleton more valuable.
Given the choice between bidding 4H and pass, I would choose 4H. However, I'm going to let partner off the hook if he bid 2H on a random 17-count with 5 spades and 4 hearts since he's not likely to make game anymore (e.g. S-Kxxxx H-KQJx, D-AK C-xx) so the suggested call is 3H.
One point here is that partner does not need to jump with 20 points anymore. When you respond, showing 6 or more points, partner needs to jump shift (or bid game) to make sure your side gets to game. Here with you having passed, from opener's point of view, your side is simply competing for the partscore and there is no reason to do more than bid 2H with 20 points. Your partner expects to play in 2H or 2S. Your raise is telling your partner that your hand is exceptional for a passed hand in that you still may have a game despite not having the suggested 26 (25) points between you. While your partner will probably go to 4 only with a maximum hand, he may realize that your hand fits very well with something like AKxxx in each major and bid a makeable game with only 16 HCP between the two hands.
3.
Hint: Do you think you can set 3H?
Answer: Your partner's first double was takeout, and the fact that he doubled again didn't change that. The opponent's bidding and your hand says that your partner is probably void in hearts. Your prospects on defense are poor; it's better to go down in 4C (or 5C if partner raises) than to let them make 3H doubled. The recommended call is 4C.
Even if you had only two small hearts so that you couldn't tell partner was short, you would still respect the takeout double and bid 4C.
If East had raised to 4H instead of 3H, and partner doubled (still takeout), you should probably pass now, hoping that partner can take 4 tricks on defense rather than 11 on offense.
4.
2D is waiting. 3D is forcing. 3S shows five spades.
Hint: Is partner's bid forcing?
Hint: Your 3S bid is unlimited so would you expect partner to jump to 5C when he can make it?
Answer: Your partner's hand is still unlimited and his 4C bid is forcing. Partner likely has more diamonds than clubs, and I would recommend bidding 4D rather than raising clubs. If partner has equal length, he can bid clubs again.
(Partner's hand is: S-A H-Q D-AKQT42 C-AKT95. If you pass 4C, you miss game which makes most of the time diamonds are 3-2. If you expect partner to jump to 5C, you get to play in a minor suit (or 5S) when your hand is S-QJ98754 H-765 D-3 C-32,
5.
Hint: Why didn't your partner reopen with a double?
Answer: You might be thinking that having the safety of having your partner know you don't have anything would allow you to bid 3H here. However, bidding 3H is only a good idea if partner has three-card support. Think about this: your partner has spades; your partner has clubs; your partner has three hearts; your partner must have short diamonds, what would they have done over 2D? They would have doubled for takeout! Partner didn't double for takeout, therefore he doesn't have three hearts. You don't have exciting distribution for play in clubs, so 3C is high enough. Your
♦J might be a stopper but you don't want to play 3NT with at most 23 points between you and no good fitting suits and no entry to your hand.
The recommended call is Pass. Sometimes when you don't have anything, you should just pass.
In fact, most of the time you don't have anything, you should pass. Problems 1-4 were the exception rather than the rule. The times when you can bid are: you believe you are improving the contract, and your bid can't mislead partner because you have either already shown weakness, or you are being forced to bid.