In a case with say {thoughtseize}
When is the last chance to respond with an instant? Can I play the one they choose as they choose it. Or must I spend it before they see my hand
You have to cast the spell before they see your hand since that is part of {Thoughtseize}'s resolution. You can't cast anything as a spell is resolving.
RESOLVED
Before they see your hand you can cast an instant as a reaction to it. Once you let it resolve and they are looking at your hand, you can't cast it to save it from being discarded
Thanks, had a feeling. Just wanted to clear it up officially first. Personally I don't like making mistakes that benefit my opponent
Opponent cast thoughtseize
Spell goes on stack
Opponent declares he is not casting instants or activate abilities, passes his priority.
Priority goes to you.
You get the chance to cast instants or activate abilities.
That is the chance to react. If you pass your priority after that, thoughtseize resolves and he sees your hand and makes your life difficult.