A response of 2♥ to 1♠ shows a 5-card suit and a minimum of 8 points.  With the South hand, you can jump to 4♥.  If by partnership agreement you are playing 'splinter bids', you could jump to 4♣ which shows a singleton or void club and heart agreement.

The only hope of making the contract is if the King of spades is with North so play a spade towards the Queen and you have a 50-50 chance of a 9th trick.  Anything else gives you no chance!

It is clear from the lead that the spades are breaking 4-4 and North must have the Queen.  There is therefore no point in finessing the Jack at trick 2.  Furthermore, if you do take a losing finesse at trick 2, look what happens if North switches to a heart.  You cannot now make the contract whatever you do.  If you play the Ace, the defence will get in with the Ace of clubs and make several heart tricks.  If you don't go up with the Ace, South will win the trick with his King and switch back to a spade which also defeats the contract.

If you go up with the King of spades at tricks 2, then knock out the Ace of clubs, 3NT is cast iron.

You can't avoid losing the Ace and King of trumps and the Ace of clubs but you can avoid losing a spade if you act quickly.  After winning the opening lead, you need to play a club at trick 2 to knock out the Ace.  Another spade will be returned so you now need to play two more rounds of clubs, discarding a losing spade on the third club.  Only now can you let the opponents in by drawing trumps.

From the bidding, partner is marked with a shortage in diamonds and with two Aces you may have the opportunity to regain the lead and give partner some ruffs.

Lead the smallest diamond and if partner is void, he may take the hint and play a club back which you can win and give him a second diamond ruff as well as making your Ace of trumps.  

If partner has a singleton diamond, it is still a great lead as when Declarer draws trumps you go up with your Ace, play another diamond, partner ruffs, plays a club back to your Ace and you give him a second ruff.  See the full deal.  Any lead other than a diamond will allow 4♠ to make.

On the spade return, you should play a diamond to the nine, then finesse a heart.  When you get in again, come back to hand with another diamond and finesse the hearts again.  Three times out of four (75%) at least one of the top heart honours will be in the North hand so unless you are very unlucky, playing this way should yield nine tricks.

With your partner having overcalled 2♥, you have an excellent supporting hand and lack of defence to spades so I would not hesitate to bid 4♥.  Bidding diamonds is a waste of time and could result in the opponents bidding up in spades before you have supported hearts.

The bad trump break is no more than a distraction.  Play the cards in the right order and you can make all 13 tricks.

You should play the three of hearts.  As you have no entry, you are reliant on partner getting in if you are to make some heart tricks.  As partner played back the 10 of hearts, you know Declarer has the Jack so you have to hope they each have one heart left and that your partner gets in.  See the full hand.

After winning the spade lead you need to play three rounds of diamonds, discarding two losing spades.  The hearts are not lying particularly well but you can afford to lose two heart tricks and the Ace of clubs, providing you don't lose any spade tricks.

1NT

As you have no entry to your clubs, you need to maintain communications with partner.  By looking at dummy's high card points, your partner is marked with between 9 and 11 points so he is bound to get in again sooner or later.  You should therefore resist playing the Ace of clubs and wait for partner to regain the lead and play another club.

If you duck the club, Declarer cannot make the contract.  If you don't duck, he will make 3NT with an overtrick.

No bid.  Despite bidding Stayman, partner's bid is a sign-off.  He will have less than 11 points and 5-4 in the majors.  He could have a very weak hand so continuing to bid is dangerous.

Partner has shown a doubleton.  At trick 3 you should play the 10 of diamonds.  You can see that dummy will ruff but hopefully partner will overruff.  If he is able to do so, you would like him to play back a heart to your King.  The 10 of diamonds is a suit preference signal asking for the higher of the other two suits.  If you played a small diamond that would be asking for a club.

If you find this defence you will make two diamonds, a spade, the King of hearts and the Ace of clubs.  Any other defence will allow Declarer to make his 3♠.

North opens 1NT, South bids 2♣, North bids 2♥.  South should now bid 2NT.  North, with 14 points can raise to game.  However, not 3NT!  As his partner bid Stayman and wasn't interested in hearts, he must hold four spades so North should now jump to 4♠.

3NT is a poor contract.  You would lose at least four clubs and the Ace of spades but in spades you would lose a maximum of two clubs and the Ace of trumps.

You should pass.  Your partner has taken you out of your penalty double of 1NT so should therefore be very weak.  Any further bidding is asking for trouble!

As East you should play the eight of diamonds.  Declarer cannot now make his contract.  If you go up with the Queen, Declarer can now make two diamond tricks but more importantly he gains a tempo.

Even if your partner held the King of diamonds and Declarer the Jack, it would still not lose anything to play the eight.

No Bid.  You have good defence to 1NT doubled.

Win the opening spade lead with the Ace, then play the Queen and Jack of spades, discarding the Ace and King of hearts from dummy.  Now play the Queen, Jack and 10 of hearts, discarding the Ace, King and Queen of diamonds from dummy.  Then run six diamond tricks and finally play the 2 of clubs to dummy's Ace.

On the King of spades lead, you need to discard a club from dummy (key play) and win in hand with the Ace.  Next play a trump to dummy's Jack, followed by a diamond which you ruff in hand.  Now play another trump to dummy's Queen and ruff another diamond in hand.  Play another trump to dummy.  Now play dummy's last trump, discarding the Ace of clubs from hand.  Then play the Ace of diamonds, discarding the King of Clubs from hand.

Having discarded the two top clubs from hand, you can now run the rest of dummy's clubs for your 13 tricks.