You tell us why the variables are affecting Cylinder two
Just throwing out all the basic stuff to look at without being right beside you while its happening
No insult or negative connotation just trying to be helpful
If two is coated in carbon/soot have you pulled the injector Cyl 2 and swapped it with another? Ive had a bad injector in a EJ25D and Ej251 do similar, the injector would essentially flood the chamber at anything above idle.
The crank sensor tells the ecu where each cylinder is/position of the crank for firing purposes, can't hurt to diagnose, if you ruled it out no need to worry with it