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Continuations after we overcall 2NT for the minors

Annie and I were practicing on BBO when the following deal came up. We bid as follows.

North
AKx
Jxx
xx
AQxxx
South
xx
AKxxx
KJ10xxx
W
N
E
S
1
2NT
P
3
P
4
P
4
P
5
P
6
P
P
P

Our agreement is that after we overcall 2NT for the minors, advancer's cuebid is game invitational or better and responder's rebid of the next step is "all minimums" with higher bids showing extra's and creating a game force. We also play jumps by advancer as "mixed" and the bid of the fourth suit (3S in this example) as natural but not forcing.

I am exploring whether there are better continuations that we should adopt. The questions below are written in the context of the auction shown above.

Please select up to 4 choices.

After (1H)-2N, advancer's 3S bid should be natural and nonforcing
After (1H)-2N, advancer's 3S bid should be forcing
After (1H)-2N, advancer's 3S bid should be "other" (explain)
(1H)-2N-3H should be game invite or better
(1H)-2N-3H should be game forcing
(1H)-2N-3H should be "other" (explain)
After (1H)-2N-3H, overcaller's 3S bid should be "all minimums"
After (1H)-2N-3H, overcaller's 3S bid should be natural (a fragment)
After (1H)-2N-3H, overcaller's 3S bid should be "other" (explain)
After (1H)-2N-3H-4C, advancer's 4S bid should be natural
After (1H)-2N-3H-4C, advancer's 4S bid should be a contol bid agreeing on clubs as trump
After (1H)-2N-3H-4C, advancer's 4S bid should be a "matched pairs" keycard in diamonds (4H would be keycard in clubs)
After (1H)-2N-3H-4C, advancer's 4S bid should be "other" (explain)

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