No one who advocates for universal healthcare is a conservative. Period.
You can advocate for universal healthcare while still having conservative views in most other subjects.
Absolutely, I'm a conservative and I support universal healthcare (but more a multi-payer system like the German model rather than single payer).
Well, when you get down to it American Conservatism is just extreme classical liberalism with a few conservative positions on social issues and law and order (and on the latter some are excessive), it's not a real conservatism, and that's why I don't really identify with the GOP (and ideally if the option were still around I'd be a conservative Democrat).