LAVENDERi

We can check all the bids first. 4H was preempt and west doubled on his own even without HA. So west was likely to have 3aces as your 3 losers. To make sure you get down, west would go on to play two black aces after you broke any black suit. The best way is to try to cross to dummy by D8 because it looks like much weaker than CJ. West might duck his DA so that you would get the only hope for this game. However, you may consider what if west just played 3aces without thinking. Then I hope God bless you XD.

When WE is vulnerable, pass for penalty；otherwise 3nt. You may consider 3H, but 3nt genarally scores better because you two have enough pts for it. You must know 3h is a passive responce which can show 0pts. You two may miss 4H even with much more than it.

(B) is easy to think. 2C...2S means your clubs have at least one more than your spades. You can't bid like that with spades as long as or less than clubs because highers score better. Just be careful of (A). 1S...3C means 4+S&4+C but not always 5+S&4+C. You can bid like that with spades as long as clubs because highers score better than minors. Moreover, (A) is absolutely stronger than (B) because (A) is at a higher level on the second responce. However, you have clubs two more than spades. For reasonable logic and for a better contract, bid the much longer suit first. Highers absolutely score better than minors when you make all the contracts. But highers can score awfully when they are much more hard to play than minors.

I will take a view on probability. Frist, we don't know what your p have. Your p can support any suit. (1)Double：There are 2 chances for your p to support your suits - diamonds or spades. (2)3D：your p doesn't always support your diamonds. It seems like double is a better bid. But you may consider what if your p bid 4H? Then you two are just unlucky. And that's how preempt bids interfers the bidding.

Of course N 100% First, the 1st bid of north was a take-out double. The most important of bidding is to find the fit of two but not just the suit of one. North seemed like a selfish player. Secondly with your responsive double, north should jump his bid to 3S instead of a passive responce 2S which promised 9+pts and 3+spades only. Didn't he know he had 4 good support and 14hcp and a useful singleton on opps' suit? North doesn't know bridge.