1) DBL - wtp ?
2) 2NT assuming it's natural and we don't play any kind of lebensohl here; I am not especially happy about it; I think I can be easily convinced there is much better option but I don't see it for now.
3) DBL - wtp again for me;
4) 2♣; If I am reading it right I opened the bidding with 7hcp and partner made t/o double (showing 4spades I guess). I can't see anything but 2♣ to be honest.
5)Very difficult without agreements because it's not clear if partner interprets our 3NT as showing extras here. I bid 3NT.
EDIT:
After reading replies:
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Yeah that makes a lot of sense to me. I am just too afraid partner has hearts and I think I have to pass 4♥ from him. I would definitely choose 4♣ playing negative free bids because then I can make a move toward slam after 4♥.
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Yeah, 3NT was 2nd call I considered. I am used to very light style of reopening though (every time with xx of ♦). Is your style of reopening different or do you bid 3NT regardless ?
I still can't believe anybody would choose anything different than 2♣ in 4th.
I am also very surprised people aren't doubling in hand no. 3; So many disasters waiting for us if we don't double (miss penalty, miss 3NT, miss 4♠ on spades 5-2 or even 6-2 if partner is weak). I really really hate 4♦. I frankly prefer 3NT and pray over 4♦. I think it's just that bad.