I mean yeah. If you associate yourself with that nation, and you wish to identify with it it, to me that's no different than when people of a certain group are proud of their predecessors(such as Alan Turing for the gay community and martin luther king jr. for the black community.) Also just because one didn't do it, doesn't mean they shouldn't be proud. A parent isn't not proud when their kid does something (like winning a spelling bee), the parent didn't participate but they're proud(depending on the parent of course)
I believe it is more related to cultural practices and beliefs, otherwise why be apart of that nation? Especially today, while it might not be easy, it certainly is easier than 100 years ago to leave your nation for another and have a chance of surviving.
Yes of course. A christian and a muslim can identify as american while still belonging to their respective religious groups. As long as you agree with national customs (such as religious/social freedom/toleration) then there's no reason to not associate with that nationality(if you wish)