That's a lot of questions, so I'll probably miss some aspects of what you're asking.
I'm not sure what you mean by "mechanism" but in general there's nothing that feels like a familiar mechanism in these quantum processes.
There's no electron inside a neutron- it's really gone. To squeeze an electron into that volume would require it to have enormous kinetic energy. Its conserved quantities, most noticeably charge, remain of course.
Massless particles (photons and gluons) have wavefunctions, just like massive ones.
As to whether quantum fields "exist in reality", that's a philosophical question whose answer is somewhat subjective. So far as we can tell, nothing exists in nature except
The apparent unidirectionality of the e+p -> 2 photons reaction is not intrinsic to the process itself, but just reflects the types of non-equilibrium collisions that we can easily make. At an earlier hotter time, when the equilibrium state had lot's of e's and p's, the process routinely went both ways.
(published on 10/27/11)