Answers: (More advanced material in blue.)
1.
Hint: Any spade bid is non-forcing. How do you feel about a spade contract if partner has a singleton?
Answer: You want to show invitational values but any spade bid is non-forcing and likely to be passed with any minimum, even with a singleton spade - a spade bid by you should show six spades here. You don't have a guaranteed fit in diamonds or clubs, and if the hand is to be played in notrump, you may have your side's only heart stopper. 2NT is a good description of this hand. If partner has three spades and is accepting the invitation, he may bid 3S on the way to game (3S would be forcing by opener after your 2NT - if partner had a hand with 3 spades, 1 heart, 5 diamonds and 4 clubs that wasn't going to accept your invitation, he might (probably should) have raised to 2S on his first rebid.)
I am assuming that you either do not know fourth suit forcing and artificial or play it forcing to game. When I saw some of the other posts suggesting that fourth-suit forcing might be an answer to this question in some parts of the world, I did some research.
Larry Cohen's Fourth Suit Forcing
He does recommend it forcing to game, but of course, he lives in the USA. If you live in a part of the world where fourth suit forcing can be made on invitational hands, then you might bid 2H, forcing and artificial, and if you do play that, you and your partner have some agreements on what follow up bids are forcing. Fourth suit forcing and artificial is beyond the scope of this thread.
2.
Hint: If notrump is right, which partner should play it?
Answer: You again want to show invitational values. 3H would do that, but partner might pass with a singleton heart and a minimum, and could raise to game with a singleton and no other good bid. (An old suit, one previously bid, at the three level shows an invitational hand when partner could be minimum.)
You could bid 2NT, but if notrump is the right place, partner should be playing it to protect his dubious stoppers like
♠Kx. It is highly unusual to bid notrump when you have neither of two unbid suit stopped.
You could bid a new suit to force (like 2D) but that will give partner the confidence to bid notrump with perhaps a singleton diamond. Worse, LHO with diamonds might double 2D and the opponents will make their best lead against any contract. (With three suits being bid, this double should be penalty-oriented; helping partner to defend correctly.)
Partner should have six clubs. You do have a club fit. While partner might expect three clubs for a raise to 3C, your
♣K is a good filler which could make clubs a running suit for your side. If partner is dead minimum and passes 3C, that is likely the best contract for your side. If partner has the top of his minimum range and stoppers in diamonds and spades, he can try 3NT. If partner is accepting the invitation, he can bid a 3-card heart suit on the way to game (he's already denied four by not raising, so you can't misunderstand.) I am recommending that you raise to 3C.
3.
Hint: If your partner doesn't accept the invitation, what is your likely best contract?
Answer: Again, you want to show invitational values. What does partner have? Opener rebidding a suit on the two-level should show an unbalanced hand. Partner shows at least four clubs. If partner is 4-4 in the minors, he either has a balanced hand that should rebid 1NT, or he has four hearts which shold raise hearts, or he has four spades which should rebid 1S. Partner should have at least as many diamonds as clubs so he should have five diamonds.
I am aware that some players bid 1D sometimes with four diamonds and five clubs and no good rebid over an expected 1 of a major response. However, with a good five-card club suit and a poor four-card diamond suit, partner should open 1C and rebid clubs anyway. Partner strongly suggests five diamonds in this auction.
You don't want to bid 2NT with the only unbid suit unstopped. You don't want to bid any number of non-forcing hearts and risk playing there with a singleton. You rate to have an eight-card diamond fit, and can show invitational values by bidding 3D, and that is what I recommend. If partner is accepting, he can bid 3H with three-card support. To more serious pairs: You want an agreement with partner whether 3S by opener after you bid 3D shows a stopper, asks for a full stopper, or asks for a partial stopper.
Pairs (probably not in the USA) who play fourth suit forcing and artificial and not forcing to game may bid 2S on this hand. I won't go any further into this because I've already told you more than I know.
4.
Hint: Can your partner have four spades?
Answer: Partner should have rebid 1S if he held four spades, so he doesn't have four spades and there is no reason for you to introduce your spade suit. You want to invite and your most likely game (if you have one) is notrump, so bid 2NT.
While you may very well want to play 3D if partner doesn't accept the invitation, this isn't the time to raise to 3D. Partner will think that there is something wrong with your hand for notrump if you raise diamonds, and you have both a stopper in both unbid suits. If partner accepts, playing 3NT from your side is a good thing. If partner declines, 2NT should be an okay contract, and some of the time that partner is more distributional, partner will sign off in 3D anyway.
5.
Hint: If you bid 3C, what will partner do with a heart stopper? Is that what you want?
Answer: You have an invitational hand. First, we don't want to rebid any number of spades (non-forcing) because we don't want to play in spades opposite a singleton. We don't want to bid notrump because of our heart weakness; if we play in notrump, partner should play it so that the lead comes up to his heart honor(s) instead of through them.
That brings us to 3C. If we bid 3C, partner with a heart stopper will probably bid 3NT (unless he has delayed 3-card support for spades - you probably shouldn't bid 3C if you're not ready for partner to show 3-card spade support.) He will bid 3NT with a dead minimum because your bid is forcing. You don't want to be in game with a dead minimum. In fact, most pairs play that a new suit at the three level in a non-competitive auction is forcing to game, because partner does frequently just bid 3NT. You can't afford to make a game-forcing bid with an invitational hand. So what can you bid?
We come back to that two-card support again. You can afford to bid an old suit at the three level as that describes your strength accurately. If partner passes, 3D will be a fine contract. If partner accepts the invitation, he might show 3-card spade support, or bid 3NT. If partner is worried about clubs, partner could bid 3H to show that hearts are stopped and you can bid 3NT.
(Partner isn't showing a four-card heart suit here because you shouldn't have four hearts on this auction. With a invitational hand and four hearts, you could have rebid 2H. There is no sense in him looking for a fit if your side can't have it.)
6.
Hint: Your partner probably has five diamonds and four clubs. What is this hand worth?
Answer: When you first started the game, you probably learned to count your high-card points and perhaps points for length. You would have counted this hand as 12 points (11 HCP + 1 for the fifth spade) based on what you were told. And that's fine, you have to be told something in order to be able to function with very little knowledge.
If you've made it this far in this post, you should have learned something about how to evaluate your hand better than just counting HCP and length. First, your side has bid diamonds, spades, and clubs. What do you think the opponents are likely to lead? If partner does not have a heart honor, your
♥QJ might as well be the
♥32. Let's think about notrump for a minute. If your partner has two hearts, even if partner has the ace and they give you two hearts on the lead, you will likely have to give the lead up at least twice and the opponents will take three heart tricks as well as two others. It's much worse if partner's two hearts are the
♥Kx as you'll only get one heart trick with your combined six HCP and the opponents will take at least four.
Partner could have three hearts to an honor. If partner has the
♥A, the fact that your
♥QJ are doubleton will likely prevent him from any chance of getting three heart tricks, and even if partner has the best holding of
♥Kxx, the opponents still know to lead hearts and will establish at least one trick for themselves, and two tricks if the opponents' hearts aren't 4-4. Note that partner should have nine cards in the minors. If partner does have three hearts, partner has a singleton spade. While your
♠K and
♠J will provide stoppers, your spade suit won't produce many tricks and your spade length is probably worthless. Suffice it to say that your high cards are not in the right place opposite partner's minor suit oriented hand. While the HCP may say this hand is in the invitational hand, you should realize that this hand isn't good enough to invite. I would call this hand a minimum hand for responder and correct to 2D. If partner makes another move as opener (which should show about 17 points), I'll cooperate, but if partner can't invite game himself after my 2D rebid, we shouldn't have enough strength for game.
You might wonder about a possible 5-3 spade fit. If partner is 3-1-5-4, your
♥QJ aren't worth anything opposite partner's singleton, and if partner has a medium hand for opener, he can bid 2S himself and you won't miss your game.