Answers:
1.
Hint: We like to have a six-card suit to rebid our suit. Is there another call that describes our strength and distribution?
Answer: We have a balanced hand too weak to open 1NT. Because we show a balanced hand, we give partner permission to 4H with any six hearts, and even to rebid 2H even with only five hearts if he thinks it will play better than 1NT. This isn't important for this problem but will because a good reason not to bid notrump on the problems in which you have a singleton heart.
Did you choose 2D because you are afraid of your lack of a club stopper? Fear not, they're likely not taking that many club tricks against 1NT, and if partner raises to 3NT, it is extremely likely that he holds a high club or enough length in clubs to make the club suit not a problem.
2.
Hint:What are our favorite games? What bid would best help us find our fit if we had one?
Answer: If you bid 1NT (see the answer to 1), partner will bid 4H on H-Kxxxxx and an opening hand; this isn't where you want to play. Our favorite games are the major suits when we have an 8-card fit. If you don't bid 1S, partner will think you do not have 4 spades, so bid your spades despite the fact that they are ugly.
3.
Hint:Even if a 2D rebid only showed five, that would show five of our cards. Is there a way to show nine of our cards?
Answer: Again, you don't want 1NT since you encourage partner to bid hearts with any six hearts, and diamonds shows a 6-card suit and says nothing else about your distribution. Look what partner knows if you bid 2C, the recommended bid. You have four clubs, but since you bid diamonds before clubs, you must have at least four of them also. You didn't raise hearts or bid spades so you aren't 1-4-4-4 or 4-1-4-4, and you didn't rebid 1NT so you aren't 2-3-4-4 or 3-2-4-4. This means that one of the minors (likely diamonds since you bid them first, but some experts will bid 1D with 4 diamonds and 5 clubs so they will have a rebid) is a 5-card suit! By one simple rebid, you have shown 9 cards in the minors.
4.
Hint: Do you have enough to force to game?
Answer: You have 18 counting length, not quite enough to force to game opposite a balanced 6-count. Partner will know that your range is 13-18 (or 12-18) and will try to keep the bidding open (perhaps by taking a preference back to 2D) with enough for game. Occasionally you will miss a game when partner has no real alternative than pass, but jumping to 3C is game forcing and while you don't have nearly enuogh to force to 5 of a minor, you expect to bid 3NT yourself the next round. There are three problems with this:
(a) You are unlikely to make 3NT opposite a random 6 or 7 point hand - your diamonds aren't that robust and where are your nine tricks coming from?
(b) Sometimes your partner is going to insist on 4H. Your hand is not only going to be disappointing in trump support but also in strength.
© The jump shift may make partner go wrong in slam decisions. For example, if partner has:
S-AJx H-KQxx D-10xx C-Axx, it will be nearly impossible to stay out of a no-play slam after showing the values for a jump shift. If you only bid 2C on your hand, partner will bid 3NT. Since he might do that with 15 or 16, you, being a maximum for your bidding with slam possible, can invite slam with a quantitative 4NT which partner will pass. If there's any chance that partner will think 4NT is Blackwood, this won't work.
Those who bid 3C get some credit for not bidding 2NT which again gives partner permission to play 4H with six lousy hearts. You could easily have four trump losers!
5.
Hint: Do you have a call that describes your strength and distribution?
Answer: You have a balanced hand and too much to open 1NT but not enough to open 2NT. A jump to 2NT shows this hand perfectly. Yes, you have nice diamonds, but if partner is interested in a diamond slam, he can bid 3D, forcing (if you play no special conventions over your 2NT rebid, any bid by responder after 2NT is game-forcing.)
6.
Hint: Do you really want to emphasize this club suit?
Answer: Technically, you do not have a balanced hand, but 2NT is very descriptive. You have 2-card support for your partner's hearts which might be the information he needs. You have spades stopped twice and enough clubs that the opponent's are unlikely to harm you with club leads.
The problem with rebidding any number of clubs is that partner will think your hand is much more oriented for play in a minor suit than it really is, and avoid notrump when it's okay. For example, partner holds:
S-xx H-AQ10x D-xxxx C-Kxx
If you rebid 3C and partner bids 3D, you can now bid 3NT but partner will know you have a spade stopper but might think it will be knocked out at trick 1 and you might have a problem taking the first nine tricks, whereas your diamond length and club filler make 5D look like a much better prospect.
Partner might be pretty surprised to lose 3 club tricks and a diamond trick in 5D after this auction. 3NT should have no problems with two spade stoppers; even if you don't find the DQ, you lose a diamond to take 1S, 4H, 4D, and perhaps a second spade on the lead.