These hands were shuffle, deal and play at San Diego Bridge Club on Home Avenue, so I don't have records of all the spots.
A card combination
First a card combination. You opened one of a minor. After pass, pass, RHO bid 1♠ and you rebid 1NT (showing 18-19 HCP opposite a passed partner) with something like: ♠A9 ♥KQx ♦KQx ♣AJxxx. The ♠8 was led and partner produced the ♠107xx in dummy (along with a couple of Jacks and a Queen). RHO played the ♠J. Your correct play is to kill the ♠J with your ♠A. Your ♠9, combined with the ♠10 in Dummy, becomes a second spade stopper. If you duck the spade, RHO will play a low spade and you'll have only one spade stopper. The Rule of 7 does not apply when you have the spots to create a second stopper by killing an honor.
A good slam
West opens 1♥ and partner's 1♠ response creates a rebid problem. A 2NT rebid with a small doubleton club is unappetizing. Jumping in very chunky 5-card heart suit lies about length, but was an option. I chose to jump shift into 3♦, even though it was only a three card suit. Partner's best rebid is a temporizing 3♠ call. I will bid 4♠. She can bid 5♣. I'll bid 5♦, and we will probably get to the 6♠ slam.
With spades 3-1, we lose a spade trick. However, declarer can pull two round of trump, ending in dummy, discard two losing diamonds and one losing club on the top three hearts, and plan to ruff the remaining low club in Dummy. When the defense is able to take ♠Q is immaterial.
Notrump slams are just arithmetic (broken records repeating)
West: ♠Axx ♥AKJx ♦KQx ♣AQx
East: ♠K10xx ♥Qxx ♦Jx ♣KJ10x
West opened 2♣. East responded 2♦ (waiting). West rebid 2NT (showing 22-24). East bid 3♣ (standard Stayman—not Puppet) and West bid 3♥. East bid 4NT. This is a Quantitative Raise—asking partner to pass with minimum and bid 6NT with maximum. I went to 6NT with my control-rich 23 HCP. After knocking out the ♦A, we had 12 tricks. Note that if partner had four hearts with me, she would have bid 4♣—which, by agreement for us, would be Roman Key Card Gerber for hearts. So, Roman Key Card Gerber when you bid the right (fitting) major. 4NT remains quantitative over Stayman auctions. (Some people choose to have a similar agreement over transfer auctions.)