Contract 3 NT by South - West  leads Queen of hearts.

The key to the solution is the distributions of diamonds.
If the odds are 3-3 there is no problem: it is sufficient to take the lead card with the K ©, saving the entry to dummy, to play the K ¨, to go to dummy and cash all diamonds. You could make 3 NT +1.
But if you find diamonds 4-2 as in the diagram not only will you lose the J , but you will not be able to cash the last diamonds, and contract will be set one.
Since only 5 diamonds tricks are sufficient to maintain your contract, sacrifice one Honour and cover your K ¨ with the Ace of dummy as your second trick, then play again Diamonds till you give up the Jack. After that, you take every return and you can cash the last diamonds, since you have still transportation to dummy with the Ace ©.

Contract 4 © by South - West  leads Ace, King and Queen of ª.

Most answers have been right as far as the refusal to ruff the third spade was concerned, but many lost themselves half way!
In fact they assumed trumps would be divided 3-3: but they are 4-2 with the four trumps in East, so South should ruff in dummy with the 8 of trump the eventual continuation of spades and overruff if East plays the 9, not ruff with the J at dummy, otherwise he would lose a trick in trumps.
Remember: when you are given the possibility to ruff a trick, always consider the advantage of refusing the ruff and discarding a loser card instead, especially when you are short in trumps, as you are in the example where you are playing 4 © with the Moysian fit 4-3.

Contract 6 © by South - West  leads the King of ª.

Whenever there are shortages in both hands you should consider the possibility of crossruffing that allows you to "lengthen" your trumps and produces a greater number of trump tricks. Pay attention to cash as soon as possible your side winners which you do not need in your planning. South will cash A,K ¨, A ª, A § and 8 trump tricks. So, after taking the initial lead with the Ace, South plays small to the Ace § and begins to ruff alternately § and ª.
But, if South forgets to cash immediately his diamond winners, West will be able to discard a diamond on the third round of spades and South, unable to draw trumps, will later lose by a ruff one of his diamond winners.

Contract 4 © by South - West  leads the King of ª after he overbid 1 ª.

The declarer should try to create an entry to dummy to cash the last diamond if the suit is divided 4-2.
So he should take with the Ace, play A,K ©, leaving one opp's master trump at large.Then plays on diamonds discarding a spade loser on the third diamond, ruffs the fourth diamond in the hand, ruffs a spade in dummy and goes on playing the fifth diamond: East can ruff if he likes but South discards the last spade loser and make his contract.
Remember this expedient of not drawing all trumps and leaving one at large. This play preserves an extra trump for declarer, (sometimes in both hands) to be used to gain a trick by a ruff or to create an entry to dummy.

Contract 3 NT by South - West  leads the 4 of ©.

The declarer can make his contract with 4 diamond tricks, 2 heart tricks, the A ª and A,K §. But to cash dummy's diamonds he needs an entry to dummy, so he has to create one playing small heart from dummy and taking in his hand with the Ace!
After that the hand has no more secrets: South plays Ace ¨ and goes on in the suit untill the King wins. The entry to dummy by means of Q,J © , will enable him to cash the remainder of his diamonds.
Remember: stop to think before playing the first card of dummy; very often the future of a contract depends on what is played in the first trick!

Contract 6 ª by South - West  leads the 10 of ¨.

The declarer can count 11 tricks (7 trumps, A ©, A ¨, and A,K §).
The missing trick could come from the Q ¨ if the King is favourably placed. So he tries to take the leading attack with the Queen, but Est plays the King and South wins the trick with the Ace.
The only possibility for South to maintain the contract is the promotion of the fifth heart of dummy, possible if both the following conditions are met: hearts must break 4-3 (p=0,62) and trumps 2-1 (p=0,78) since he needs 3 entries to dummy represented by dummy's trumps.
South plays then hearts to the Ace and ruffs a heart with the Ace, goes to dummy playing the Queen of trumps to the King, ruffs another heart with the J of spades; now plays the seven of trumps for the 9 of dummy so he can ruff the fourth heart with a high trump.
He may go to dummy playing the 2 of trump covered by the 5 and may discard a loser diamond on the fifth heart.
What is the probability of making the contract after the first trick has been played?
Since both conditions have to be satisfied at the same time (spades 2-1 and hearts 4-3)

the final probability is given by the product of the probability of single events, that is: p=0,78x0,62=0,4836.
Nobody answered right so I couldn't assign the extra 3 points....
But, since I'm very good at heart, I'll give  6 extra points (3 for each questions) to all who tell  me:
1. What is the probability to make 6 S, before East played the K ¨ on the first trick;
2. What is the probability to make 13 tricks before East played the K ¨ on the first trick.
Answers have to be sent to me within Sunday the 28th of January!
Love all