I think the concern is generally air coming from the bleed air system (air that has been redirected from the engine core's compressor stages, prior to combustion) which is used to pressurize the plane. This can come from either the main engines or the APU, but in-flight it's almost always going to be the main engines and the APU will be shut down. During a potential fume event, if the APU is supplying bleed air the packs could generally just be turned off, the APU shut down, or the aircraft deplaned, since it's probably on the ground. Obviously you don't have any of those options in the air.

Exhaust, which is what you're smelling when the doors are open, seems like it'd be much less of a problem. Any fumes will be much more dilute from all the uncontaminated air pushed by the fan through the bypass ducts, and of course diffusion into the environment. Not to mention probably decomposed by the temps in the combustion chamber. The bleed air though comes from the engine core's compressor stages (before combustion), and it's the only source of air for the cabin, so if it's contaminated you won't have any dilution effect.

Both. You smell fumes while rear doors are open because the APU is not moving (or there is another plane in close proximity). From the main engines, it should not be noticeable in flight