Benny, it depends on the exact regional accent. In my opinion, something in between would be the most “standard” — just imagine the doctor wants to look in your throat. Rachel’s pronunciation sounds like it is heading a tiny bit in the direction of the RP pronunciation — you’ll hear that a lot in Canada (although I believe she is American). Your second video demonstrates a sound that significantly fronted — that is characteristic of the Chicago accent that Debbie tells you she is teaching. I would definitely *not* consider Chicago accent to be the most standard (even though I can imitate it pretty well), although you will hear a similar accent in Milwaukee, Detroit, Buffalo, and Rochester. Watch out for her pronunciation of the “a” in “mat” — standard American accents only use that tensed sound if the syllable ends in /m/ or /n/.

Phil gave an excellent answer. #1 - I hear a completely acceptable [ɑ]. #2 - I hear an unusual vowel which is probably [ɐ].

Short "o" and "ah" do sound the same, like in rob or slob. Neither of the lips sentences is common, I am not sure what you are trying to say.