None of the above. No one pronounces "aw" like the a in Apple. And most people do dinstinguish between "a" and "aw" by pronouncing the latter more like the a in "awe".
"pa" would be pronounced between these two, depending on speaker:
/pɑː/ — if I had to use "normal person's IPA", "pah" would be my attempt. This, to me, is the more common pronunciation. Should rhyme with "bra" … assuming you pronounce that like I do.
/pɔː/ — like "paw" or "awe". This is a region-specific dialect, to me. This appears to be the one you're familiar with.
If papa is a stand-in for father, I'd pronounce it with a long a, as in father. If papa is a stand-in for grandfather, I'd pronounce the first a as in apple, and the second as in paw. But of also spell it papaw. Seeing 'pa' in its own, I'd never think it was pronounced like paw, unless I was reading something written in Hungarian.