[cencio]

1) When playing 2 nt jacoby, how to bid the true 2 nt ( 10-11 points and a balanced hand)
2) after 1 bid, 1 bid, pass, pass: how the opener must declare with various hands

[Stephen Tu]

(1) If playing 2/1 GF, you bid 1nt then 2nt normally with a natural 2nt (or raise partner's major if they rebid it showing 6, e.g. 1s-1nt-2s-3s, if you have a couple spades). If playing standard, then you'd typically bid a 2/1 then 2nt. Some 10s you might not invite with, either system.
Note that you do this even when *not* playing Jacoby, typically, as in American based systems 1 suit - 2nt was typically played as a natural game force (13-15) before Jacoby became popular.


(2) If your opening bid is overcalled, what your call is depends on your shape, strength, and the level of the overcall. At lower levels, typically one passes with minimum hands with length in the overcalled suit, bids 1nt with 18-19 balanced and the opp's suit stopped, doubles with support for other suits and shortness (2-) in the opponent's suit (catering both to finding partial in another suit, and to partner wanting to pass the double for penalties), or sometimes rebids one's own suit with extra length (6+), and sometimes bid a new suit with like a 5-5 or something like that.

[Douglas43]

I would just add to Stephen's post, in case you are playing weak no trump

(2) if playing a weak no trump (say 12-14), 1NT could be less than 18-19 to cater for hands that 2/1 players would have opened 1NT.