1. Yes, "stormy" is fine here – it would probably be more usual to say "they have a stormy relationship".
2. "My first lover" implies a sexual relationship; "my first love" doesn't specify.
3. "She is not my type" is fine; it will be taken to mean "not my physical type" by most people. "She's not my kind of girl" is much vaguer, and would take its colour from the context.
A cheery Saturday night to you too!