The answers (I am assuming IMPS or rubber bridge and Standard American or SAYC here):
1.
Hint: Do you have a game? Where is the safest place to play?
Answer: Partner should not have more than 16 points counting length (some would say 15), and if your partner counted club length, you know that he is likely to have overestimated that length. (For example, his C-Axxxxx would be a lot better if you had three small than here where you hold a singleton. If you're a true beginner and don't understand, ignore that statement, the discussion still makes sense without it.)
Your partner has a minimum opening hand and you have no game. You want to play in a safe low spot. Two minimum hands should attempt to stay below 2NT unless pushed by the opponents.
First, you can ignore the spades. Partner with four spades would have bid them rather than rebid his clubs so you don't have a spade fit.
Second, if you rebid the hearts, you will likely play there regardless of partner's lack of support. If partner has three hearts, great! However, far more often, partner will have a singleton or doubleton and 2H will be an awful spot.
Third, you might think that could play 2NT, but that's wrong on many counts. First, it invites game, so the only time you'll make 2NT is when partner raises to 3NT, down 1. It shows about 11-12 points. Even if you could bid 2NT as a final contract, which you can't, would you want to? With the misfit, neither your hand nor partner's is going to have a lot of entries. Having a long trump suit will help the hand with those trumps get in and take the tricks in that hand.
Partner should hold six clubs for the 2C rebid. Partner virtually always has a better rebid than 2C with only five (1NT on a balanced hand; raising hearts, or bidding spades.) The 6-1 club fit isn't perfect but it rates to play better than anything else; partner will be able to score some of his small clubs either by ruffing or after drawing trump; where partner's club length isn't that likely to be useful in any other strain.
Pass 2C. It may be your last makeable contract.
2.
Hint: Do you have a game? Do you know where you want to play? How do you find out without risking missing a game?
Answer: Here, with 14 HCP (15 counting length) opposite partner's opening bid, you want to reach game. Since partner doesn't know you have such a good hand, it is your responsibility to reach game, either by bidding it, or making forcing bids until game is reached.
If you knew the right game, you would just bid it. Do you?
You certainly have a club fit, but 11 tricks is a lot to take. It would be better to try to take 10 tricks in hearts if you had a fit, or 9 tricks in notrump if partner could prevent the opponents from running roughshod in spades.
So, just bidding a game is not the best option; you need to make a forcing bid.
Is 2H forcing? No, an old suit at the two level shows a minimum hand; for repsonder, that's about 6-10 points. Opener could pass. Since opener might pass with a singleton, it also shows six hearts.
Is 3H forcing? No, an old suit at the three level shows a medium hand; for repsonder, that's about 11-12 points. Again, since opener might pass with a singleton, it still shows six hearts. When partner could be minimum, an old suit bid is not forcing.
If an old suit is not forcing, you must bid a new suit to force! Here, you bid 2D. You don't intend to play in diamonds but partner will bid again.
Note that the opener has already denied four hearts (he would have raised immediately with a heart fit) and frequently responder is looking a 5-3 fit so opener should support responder's first suit (when it's a major) with three cards. This is a high priority - so high, in fact, that if partner doesn't support hearts now, you can assume that partner doesn't have three hearts - so there will not be a need for you to ever bid your hearts in the auction without support.
(An aside for more advanced novices - beginners can skip this: If you do bid 2D to force and later bid 3H without opener having supported them, you are showing six and making a forcing bid. Why six? Because as we just showed, partner doesn't have three when he doesn't show delayed support on his third bid, so there is no sense in rebidding your five-card suit. Why forcing? Because if you had six hearts and an invitational hand, you would have rebid 3H, showing 6 hearts and an invitational hand on your second bid.)
Beginners, you're back in the discussion!
So, when you bid 2D, partner will show 3-card heart support if he has it. You'll then bid 4H.
Partner could have: S-Q4 H-Q105 D- AQ C-QJ9743. 4H is a fine contract where 5C loses two spades and a heart and 3NT loses at least five spades and a heart.
If partner doesn't have three hearts, partner will probably bid notrump with spades stopped; after all, he thinks you have hearts and diamonds and he has clubs.
Partner could have: S-KQ4, H-32 D- A5, C-QJ9743. You have 8 tricks and can easily promote a spade for the ninth. 4H could easily lose 3 trumps and the SA; and 5C will go down if you lose two hearts. Partner rebids 2NT with this hand which you raise to 3. (For advanced novices: Partner could bid 3NT with this hand but I prefer 2NT in case responder wanted to show a game-going hand with six hearts, where I'd want to play 4H. If opener bids 2NT with this hand and responder passes, it probably isn't more than a 50% game anyway.)
Partner might not have either a spade stopper or three hearts. In that case, you'll have to hope he can make 11 tricks in clubs.
Partner could have: S-74 H-A D-AQ42 C-Q109743. Partner will raise your diamonds, but you'll just bid 5C. Note that this time 3NT and 4H are both terrible contracts but 5C almost always makes. Why didn't partner rebid 2D the first time? That's fodder for a later thread. The important thing here is that you understand that you know you have game but you don't know where you want to play, so you have to invent a forcing bid to get more information from partner.