Consistency, Thy Name Is Not Editor

Q1: Would you please explain the difference between the YA and Teen categories, and itemize the grades that correspond?

Most people I know use YA and teen fairly interchangeably.

But you're really over-thinking this. The thing to remember when you're having a little obsessive freak-out about age range terminology is this: there's no secret dictionary that book professionals have agreed upon. When someone in the business says "chapter book", they might mean ages 6-9. Or 5-10. Or 3-7. Or they might be talking about any book with chapters.

So don't worry about this stuff too much, ok? If you want to be safe, you could just reference the ages that you think are applicable. And as long as you don't think your rhymed picture book about trucks is "middle grade" and you don't say you've written a "fictional novel", we have reasonably forgiving expectations of how closely your terminology matches ours.

Q2: Would a novel with a prevented-suicide subplot (grade 9 characters) be too dark for grades 7-8? Would it fall into YA or Teen section?

No. Yes.
That is to say, yes, it would get shelved in the YA/teen section. And no, it would not necessarily be too dark for 7th- and 8th-graders. They shop in the YA section all the time.