I can’t answer #1, but…
Not in the slightest.
Full disclosure–both my Ds had double majors (with math being one of their majors in both cases) --not to help with medical school admission, but to provide a better Plan B option had they not have gotten accepted to med school.
Although having a med school adjacent to campus might make it easier to find clinical volunteering opportunities–or not because you’ll be competing against all the other Duke pre-meds for those clinical positions–having med school associated with your undergrad won’t make a substantial difference in the quality of your application or your ability to gain an acceptance to med school.
If you want to see how many applicants (sorted by ethnicity) came from Duke and Rice last year, there’s a chart here:
https://www.aamc.org/data/facts/applicantmatriculant/86042/factstablea2.html