After reading this Part you are WAY past due for a COMPLETE disassembly and cleaning - and this includes removal of the firing pin - along with everything else so it looks like an 'exploded' parts diagram on your bench !but I have put at least 8000 rounds through it since I bought it,probably a bit more.
You need to do this first before anything further, guessing or speculating.
.22 ammo is very dirty as it is very possible you are getting occasional 'cushioning' of a round due to carbon buildup, then on the 2nd try the round chambers solidly enough to fire.
Also it is possible the snap you are hearing and the smoke from the chamber is due to excessive carbon buildup inside the chamber and is slightly blocking it causing back pressure. I once saw a .22 rifle so dirty the bullet jammed and the pressure ripped the rim off the case.
It is very likely after after a complete break down and intense cleaning this problem will be gone.
Most likely exactly what I recommend.And what would Henry typically do in that situation?