Bid 1NT - your partner changed suit at the 1 level (showing 6+ points) so 1NT shows 12-14 points, a balanced hand and stopper(s) in Spades, given right hand opponents overcalled 1♠. Bidding Double would be a support double, and would show 3 cards in Heart.

3) What's your rebid?

Your partner changed suit at the 1 level so 2NT would show 18-19 points, a balanced hand and stopper(s) in Spade as right hand opponent overcalled 1♠. You have a stopper in Spade but you only have 12-14 points. So 2NT is not the right bid. Double wouldn’t be right either as it would show 3 cards in Spades; and you don’t that have either.
You need to PASS. Be aware that when partner changes suit and opponent passes you must respond as his hand in not (points) limited. BUT, if opponents overcalls, you can pass, as bidding returns to partner and they can continue bidding. Your pass tells partner that you’ve a minimum opening without 3 or 4 cards in Spades (with 4 cards in Spades you’d bid 2♠ and with 3 you’d Double, which would be a support double)
A common mistake would be to bid 2NT because of Heart stoppers. That could be too high if partner has a minimum hand; if partner has 6-7 points, opponents will have more points than you, and 2NT would probably fail. If partner has more points, when the bidding returns to them they’ll be able to bid on. For example, partner might choose to Double which would be a ReOpening Double; and then you can bid 2NT showing your Heart stopper (bidding pass on your second bid showed minimum points, meaning this bid doesn’t show extras).

4) What's your rebid?

Correct Answer: Pass

Bidding 1NT after partner passes requires 18-19 points. So in this case you should Pass.
Bidding 1NT here is a common mistake as you’ve a good Spade holding. But partner promised nothing and opponents clearly have more points that you do, meaning 1NT will fail (you’ve 13 points and partner has a maximum of 5 meaning opponents have 22 points or more between them).

5) What's your rebid?

Your partner changed suit at the 1 level so 2NT would show 18-19 points, a balanced hand and stopper(s) in Spades as right opponents overcalled 1♠. 2NT is the right bid as you’ve a stopper in Spades and 18-19 points. Bidding Double would be a support double, showing 3 cards in Hearts, which you don’t have.

6) What's your rebid?

Bidding 1NT after partner has passed, requires 18-19 points and stopper(s) in Spade. You’ve got it – bid 1NT.
A common mistake would be to bid 2NT as you’ve a strong hand. But, as partner passed your opening bid, you don’t have game; partner has a maximum of 5 points so you have no more than 23 points combined) and 2NT could be too high if partner has only 0-1 points.

7) What's your rebid?

Your partner changed suit at the 2 level (showing 10+ points) so 2NT would show 12-14 points. But as you have 18-19 points and as right opponents overcalled 2♠, you should bid 3NT – your hand is balanced and you have stopper(s) in Spades.

8) What's your rebid?

10) What's your rebid?

Correct Answer: 3NT

Rebid 3NT, which shows (after partner has changed suit in 1 level) an unbalanced hand with a long solid Diamond suit (if you open 1♣ and rebid 3NT, it would show a long solid Club suit). This bid shows the same shape as a 3♦ rebid (15-17 and 6 cards in Diamond) but with a better hand; either stronger by points (as in this case) or with longer Diamonds. As opponents bid 1♠, it also shows stopper in Spades.
Note that this bid is not sign off.
Partner can pass with a weak hand, leaving bidding at 3NT. But they can also try a Diamond slam if they have a good hand and fit (or correct to 5♦ if they think it’s a better contract than 3NT).