2H-3C-3H-3NT

2H: Preempt, 6 H.
3C: Forcing one round, 5+ C, game interest
3H: Waiting
3NT: To play

1D-1H-1S-2C-2NT-3NT

1S: 12+ HCP, 4 S (cannot be 5 else would open 1S)
2C: Artificial, gameforcing
2NT: 12-15 HCP, C stopper. With 16-18 HCP, bid 3NT
3NT: To play

1S-2D-3C-3H-3NT

2D: 10+ HCP, 4+ D, may have S support, Forcing
3C: 15+ HCP, 5-4 S-C, Gameforcing
3H: Natural 4 H. With 5+, bid 2H instead of 2D
3NT: To play

1H-1S-1NT-3S-4S

1NT: 12-15 HCP, exact 5 H(else would 2H), no 4card S

3S: Invitational, 6+ S
4S: To play

1H-1NT-2C-2S

1NT: 6-9 HCP, no 3card H, no 4card S

2C: 12-18 HCP, 5-4 H-C, non-forcing
2S: Undefined/Partnership agreement

*If 2S was 2D, it'd be a self-sufficient diamond suit playable with minimum support from partner. To play.



AQxx - Jxx
Finesse the Q against the K on the first round. Do not finesse the J as you don't have T or 9. If the Q holds, cash the A and hope the K falls.

KJxx - T98x
Finesse against the Q by leading the T and letting it run if the next opponent plays small. Do not finesse against the A. Finesse against the Ace only if you have a singleton in the other hand and can ruff. However, sometimes when you have singleton, you can still choose to finesse against the Q, because if it works the K can provide a discard elsewhere. If this sounds abit confusing, consider this case:

S AKx
H KJx

S xxx
H x

Finessing against the Q usually has higher chance than that against the A. So if you finessse the J here and it works, the K can be used to discard the spade loser. If you finesse the K and it works, you also reduce your losers by one. So you take the finesse with a higher chance (J). Unless you don't have other losers or no entries, then play towards the K.

Axx - JTxx
Cash A and play towards JT. This play loses only when KQ is sitting after JT. All other layouts (split KQ and KQ sitting behind JT) yields at least 2 tricks. Finessing twice by leading the J will never work. Cashing A picks up singleton honour anywhere.

AKxx - T98x
Cash the A and finesse by leading the T on the second round. If the finesse fails, the last honour will drop on the K. If T is covered then you only have one loser.
Alternatively, you can cash the A and play small to T, conceding one trick.
Both lines of play catches everything except for QJxx and QJxxx sitting after the AKxx. They work equally well. In fact, I'd prefer the second line since you need an extra entry to get back to the hand to lead the T.