a) The belief that humanity will benefit more if nations* will live separately rather than mixed in larger, multinational countries. In a same way how it's better when family lives in it's own house, not in communal apartment with many families cramped together.
Actually that could also describe what our far-right parties today call "ethnic pluralism". That I don't find that problematic in itself, the controversial part is - as you said - in the enforcing of such a thing and in the question of equality.
"Who is qualified to be a nation member?" I would suggest that anyone who lives in a country/nation permanently should be qualified.
That's bascially the American model. Also, in theory, the French model, though the French also pretended that everyone who lived there was also culturally French. Historically the German model (similar to many other European countries) was, you're a nation member if you're ethnically German, no matter where you live, even over many generations. In recent years we are transitioning from the latter model to yours, but the concept of ethnicity had such a lasting impact that it will take quite some time to have that broadly accepted. (Politically it is accepted, but in the public conciousness I don't think so yet.)
Today I'd say it is quite easy to change your nationality (in the sense of citizenship), but you cannot change your ethnicity on your own. Ethnicity is an interesting construct in that it doesn't depend on your own perception much, but mostly on the perception of others. Your ethnicity can of course change, but that requires some generations worth of cultural assimilation and - most controversially - your physical appearance may play a role, which is where all the really bad stuff begins.
So yeah, the problem is to actually define what a nation is. Is it determined by territory, culture, ethnicity, religion (historically the case with Jews and sometimes Catholics vs Protestants), common history, a common idea, a combination of all of those?
It's basically an endless source of conflict and controversy.