Answers:
1.
Hint: With 11 points, you would normally invite. Is this hand worth 11 points with this auction?
Answer: While you have 11 HCP, when you picture how your hand fits with partner's, it's not pretty. Partner has a doubleton or shorter in least one black suit so your black high are likely close to useless. Other than the ace, your trumps are poor so there is a lot of potential for trump losers.
Picture some hands where partner might accept a game try opposite this hand:
S-85 H-KQJ3 D-AK763 C-92; This is a maximum 2H raise, yet you have four inescapable losers in 4H plus a potential diamond loser. In 3NT, you need the queen doubleton of diamonds, not a good game. 2H is plenty.
S-K85 H-KQJ3 D-K7632 C-5; Now I've made your spade honors useful. Partner can't have any more; if the
♦K were the
♦A, partner would have raised to 3H. In 4H you lose two black cards and at least two diamonds. In notrump, even if you get a spade lead to the ace and a spade continuation and the
♦A is onside, you will only score two spades, four hearts, and a diamond before losing the four top tricks and either a second diamond or the fourth spade. If the opponents set up a club trick for you, that's still not enough.
S-K85 H-KQ86 D-AQT9 C-64; This is about the best dummy you can see on this auction opposite your hand. Still, 4H requires a 3-2 heart break and a diamond finesse. Because partner has the
♦10-9 (both are needed because your jack can be covered), 3NT will also make with a working diamond finesse and a 3-2 heart break; however if clubs are 4-4, you can still win a spade trick if hearts are 4-1 but the diamond finesse works.
Game requires a lot to make here, and as you can see, even 3H or 2NT could be too high on some of these maximums, and will more often be too high when partner doesn't have an accept of a game try. I recommend you pass 2H.
2.
Hint: Is it possible that partner doesn't have four hearts?
Answer: Even if partner virtually guarantees four-card support with his raise, there will be instances in which all other choices are less palatable than a raise on three cards. For example,
S-2 H-Q65 D-KQ43 C-AQ865, rebidding the clubs risks playing in a 5-1 fit since responder almost always passes this auction with a minimum without six hearts, and 2D should show extra values (a reverse) because you are forcing partner to go back to the three level to return to your first suit. 1NT would be ridiculous with a singleton spade. So partner bids 2H with this hand, and if you bid 4H, you risk losing three trump tricks and a spade (and possibly a club on a club lead.) You can bid 3NT to cater to the fact that partner may have needed to raise on three cards. Partner knows you have four hearts and can return to 4H with a real fit.
What about bidding spades? If your partner might raise hearts with four spades and three hearts, then you may need to bid spades here. I don't recommend that approach; in fact, if I bid 2S, most of my partners would interpret it as a game try in hearts needing help in spades.
That being said, some posters have pointed out that 4S may play better than 4H if you have two eight-card fits. While I don't disagree, I think that bidding 2S helps the opponents defend on the hands that your partner does not have four spades, and most of the time, both eight card fits will take the same number of tricks in either trump suit; i.e. any heart losers will have to be lost in spades also. Bidding 2S is going to get you a diamond lead most of the time because it's the unbid suit (assuming it isn't a game try asking for help) and if partner has no diamond honor, that appears to be a pretty deadly defense.
I recommend 3NT.