Answers:
1.
Hint: How well have you described your hand? Could you have far less on this auction?
Answer: You have not described your hand within a narrow range - you could have had six points and four spades. In spite of the fact that you could have six points, partner bid 4S to make. Partner should have about 20 points and you should have enough for slam. If you know Blackwood, you can bid it to make sure you're not missing two aces; otherwise just bid 6S. Your partner's bid can't be a closeout because your partner has no idea how strong you are.
2.
HInt: Have you described your hand within a narrow range?
Answer: This time your partner knows that you have 19-21 points and has bid a game based on that knowledge. You described; partner decided. His bid is closeout. If you have enough for slam, it's partner's job to bid it after you bid 2S. You should pass 4S.
3.
Hint: What has your partner told you? Is his bid a final decision?
Answer: You have limited your hand to a narrow range; and your partner decided that game is the correct level. However, his bid is not closeout - he has shown four hearts and is giving you a choice between 3NT and 4H. Sometimes you are stuck for a rebid and feel that the best bid for the hand is a 3-card raise even if you "promise" 4-cards, and your partner is catering to that possibility. You have a clear preference for playing with hearts as trump and should bid 4H.
4.
Hint: Have you described your hand within a narrow range?
Answer: This hand may look familiar to readers of this forum. It was in a different thread and the poster asked what the opener should rebid after the 1S response. Enough posters bid 3S as opener that I thought I could pose this as a problem. Let's say you bid 3S, inviting partner to bid game. You described your hand within a narrow range, partner decided. Imagine the folly of bidding on: your partner could have passed 3S so essentially you are giving him a choice of playing in 3S or 5S but never 4S. Your partner might have stretched to bid 4S. Most of the time that there is a slam, partner would have already looked. Bidding on could cost you a game bonus if your partner can't make 5S. Since you were the describer, your partner's bid is closeout. Pass.
5.
Hint: Can partner have enough to make a slam?
When your partner bid 3NT, he expected you to pass. However, you have a good 18 point hand (counting one for the fifth club) and partner could easily have bid 3NT with 15 points. You could have enough for a slam, and since partner should have at least an opening hand, a four-level contract should not be in danger. Bid 4NT to invite a slam. (Note: with no suit agreement, 4NT should NOT be Blackwood (ace-asking) here; it is simply an invitational bid saying that you think there could possibly be a slam despite your partner's attempt to sign off.)
Your partner's bid isn't purely signoff because you have only narrowed your hand down to a 13-18 (perhaps 12-18) point range which is pretty wide.
6.
Hint: Does partner know what you have?
Answer: Your partner heard that you have a decent 7-card heart suit and not much else. Having that information, your partner decided that 3NT was the best contract. Perhaps partner has something like:
He has nine tricks in notrump but can't make 5D or 4H, and he has a good idea that this is true. If 4H is the correct contract opposite your hand, it was your partner's job to bid it. Bidding 4H shows a total lack of confidence in partner. You should pass and assume that partner knows what he is doing.