Trump's the kind of boss who hires people for specific tasks and when those tasks are complete they part amicably. So even if he wouldn't invite Pence to 2020 (which I'm p sure he will) I don't necessarily think that would reflect poorly on Pence.
Stuff like his doc.
I think they prescribe HRT. Few of them offer mamograms I think (cis dudes can get breast cancer too, risk is higher on estrogens/for MtF trans).