Re: 1.5 generation
That's an excellent point. I was trying to figure out what was wrong with this whole discussion, and then I realized it was the noun.
I'm a first-generation American, since my mom was born in Poland. I'm not a first (or second) generation immigrant. My mom was the immigrant, although she was less than a year old when she came to the US.
However, I do think it's common, I think, to talk in sociological terms about first- and second-generation immigrants when you discuss assimiliation.
I'm terrible at doing those COCA searches, but perhaps one of you with more skills that way could see how often the term "second-generation immigrant" is used compared to "first-generation" and then see how often those terms are used wtih "American"instead "immigrant."
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.