Your partner has doubled and you cannot pass as NORTH has passed. So bid your best suit giving preference to a major.
You have 19 HCPs and you want to be in game (maybe slam) but your partner has passed so you do not know if you have a fit but you know they have less than 6 HCPs, so take it slowly and bid 2H
You have 11 HCPs and 4 diamonds and 5 club cards. You can open under the rule of 20 (add the number of cards in 2 longest suits to HCP total and if >20 you can open). Clubs is your longest minor and you have no 5 card major, so open 1 Clubs.
As NORTH has passed and you have 9-11 HCPs, no 4 card major and a stopper in SOUTH's suit you should bid 1NT after your partner has DOUBLED.
As WEST has interfered with 2S after your partner has opened 1H and you do not have hearts or spades, but have 14 HCPs, so your bid is X
Your partner has overcalled and should have > 10 HCPs, 2 of top 3 honors in spades. You have stoppers in hearts and 13 points. This is enough to invite partner to game in 2 no trumps.
You have 10+HCPs your partner assumes that you have 4 hearts after their 1C bid. To tell them that you have 5 hearts you 'lie in a minor' by bidding 2D.
Your partner is saying that they have diamonds and 4 hearts. You can now add in 3 shortage points so bid 3H and invite to game.