1. I don't understand why anyone would play a carding method that required the 9 from J95, but that's not especially relevant here.
As it is, regardless of which card one should lead from J95, the more pressing question is why anyone would think it to be a suit that one should lead. To me, a nightmare lead would be Jxx Jxx Jxx Jxxx: after 1N 3N, I'd want to puke before making the lead.
So I am going to project my distaste for the choice of J9x as a lead and take the hook.
2. RHO doubled because he thought he could beat us, or that he could make 4
♥. AQx makes sense from both points of view, while Ax doesn't.
I once read that there is a special place in hell reserved for those defenders who lead a stiff trump, altho that is not of universal application. However, leading a stiff trump on this auction makes a heck of lot more sense than leading small from Qx. In any event, by ducking I am giving them a trick, with Qx, that he was almost always going to score, on the auction, if I were to have tackled trump myself..tho I haven't gamed the play thoroughly.
I assume that finessing was wrong on both hands, since I think that finessing is so clearly correct that I wouldn't have posted this as a problem

I say that half in jest since experience persuades me that bridge players rarely exhibit unanimity on any question.
'one of the great markers of the advance of human kindness is the howls you will hear from the Men of God' Johann Hari
1NT-3NT