No, "unchi" simply has the same singular and plural form.
There are no nouns in Romanian that follow the -i/-ii/-iii pattern. Most nouns that end in "-iii" in their plural articulated form, end in "-iu" in the singular unarticulated form (the only exception that comes to mind is "copil" - "copiii").
Unchi is uncle.
Nea followed by someone's first or last name is used address an older man in an informal way: nea Vasile. It could be your uncle, it could be your neighbor, or someone like the butcher etc. but you don't use it to address a teacher, an institution worker, a doctor unless you also know them personally.
No :) I do nothing like that. And I was disliked by my Romanian language teachers throughout school because I didn't like literature and writing essays. I like grammar and semantics though and I'm quite analytical myself so I enjoy explaining these things.
I have seen very interesting questions asked around here, things that we never really get to think about why we use them - they just make sense for us.