Once South opens the bidding with 1NT, North has to establish how many hearts South has.  Stayman does not work and transfers will not help, so we go back to our earliest lessons, 3♥ asks partner to bid 3NT with only two hearts and 4♥ with three or more.  15 opposite a maximum 14 points is 'a bit dodgy' for 6NTs but a heart slam is more appealing when we find partner with a fit.  4NT asks for aces and partner turns up with two.  We would have liked to know which two, ie the ♣A would be more use than the ♠A. Those playing Roman Blackwood have this information.

Remember contracts don't always make and it should not stop you from trying a slam or game if you think it might make.  It is usual to bid 50% slams.

East should lead a spade, if he leads the ♣A the interest has gone from the hand.
The contract can be made in two ways. 
1)  Win the first trick with the ♠K, Cash 2 top diamonds, ruff a diamond, ruff a spade back to hand and lead a fourth diamond, over-ruffing East with the trump ace.  Cash the ♠A discarding a club, and draw trumps, give up a club.  I said this was a lucky hand.
2)  The second method is less obvious and you have to guess where the club ace is and finesse.  On this occasion, it is better to lead the jack from dummy and hope that West will cover with the Q or better still the ace!  If neither appears, it is less likely that west will have the ace so it is better not to play the king.  Of course, tricky players holding Axx might hold up hoping you will finesse into partner’s queen.  This play would be unlikely to cost. Unless north started with a singleton King but by this stage of play you should have a count of the hand.

Some players might chose to respond 2♦ rather than 1NT on North's hand, the disadvantage being that partner might expect a slightly stronger hand for this.  Playing Acol and only 6 to 9 points you should respond 1NT and limit your hand imediately.

After East has overcalled, South can pass and wait for North to describe his hand a little more.

North should re-open with 2♠ if he has 3-card support and not much else.  With better than minimum and 0-2 spades he would either bid his own suit or double.  Playing duplicate or swiss pairs it is usually not wise to let the oposition play in a contract at the 2-level.  When playing teams don't force the oposition who might suddenly find and bid a making game.

What is West's best opening lead?

Before making your opening bid, you should plan your rebid, first or second in hand you promise to make two bids.  15 HCPs and 5 losers is a pretty good hand.  Opening the lower minor and rebidding diamonds will show a good hand.  East overcalls 1♠ leaving South with a problem.  

You can pass in this position but you must be able to trust your partner to re-open the auction either with a bid or a double.  South wants to tell North about his four hearts, to bid them would show a 5-card suit.  The correct bid is double, showing 4-cards in any unbid majors and at least nine points.  

West should raise the anti and make it harder for NS to find their contract by raising East’s overcall one level.  North shows a better than average hand by making a reverse bid, as well as more clubs than diamonds and denies four hearts.  

South knows they have enough points for game and with his spade cover ends the auction with 3NT.

We all love a slam but its still more obvious how and when to bid them when you see the hand records afterwards.  This is a fairly obvious one but we still missed it - in fact only 3 pairs bid it.

The auction may go in two different ways, East may decide to may a delayed game raise and try to find out more from West before deciding where the final contract should rest.  An alternate auction might go 1♥ from West, 4♣ from East.  This would show imediate heart support and set the trump suit, a singleton ♣  and slam intrest. West with17 HCPs can ask for As & Ks and sign off in 6♥.  Can it be defeated?   I don't think so.  North will lead a black suit, posible the ♠9.
West draws trumps in two rounds ending in hand. cash the 2nd spade winner discarding a diamond, ruff a spade, return to hand with the club and finesse the diamond which loses.  Souths best exit is a diamond to the A but West has total control and ruffs a diamond back to hand, discardingthe last diamond on a club.

West has a poor 10-count and really shouldn't be tempted to open the bidding first in hand.  After three passes South opens 1♥ and West can now overcall 1♠.  Although North only has 4 points he should support partner and bid 2♥.  East also has support for his partners overcall and bids 2♠.  South  ends the auction with 4♥.

South loses two clubs and diamond.  The secret to this hand is North supporting ♥ early.  His meager 4 points are about the best they can be, he has a singleton in the opositions suit so he does not want to defend a spade contract and if he passes now the auction may end before he gets a second chance.  South should be listening to the auction and be aware that EW have 8 or more likely 9 spades and with first round control, hopes to be able to ruff his two spade losers in dummy.

It looks like the auction is the key part of this hand - 6♣ is trivial on any lead with the losing heart disapearing on the ♥K, just a spade to lose.  Of course you will have to be careful with entries etc.

Cue bidding should get ou to the right spot.

To be finished later.

I've thought about this hand for a while, making a grand is easy only because two finesses are working.  Missing three kings you probably should not be bidding seven.

Its very tempting to respond 1♠ on Souths hand but that makes it so much harder to bid a slam.  You know you are going to play in hearts so start on the right course and tell partner the good news and agree hearts as trumps.