A few questions about interviewing for a new job?

1. Is it okay to dress up a nice pair of jeans if I am interviewing at a casual company, a place where jeans and a shirt would be appropriate attire?

2. Should I really send a thank you note to the person who I interviewed with? Do people still do that?

3. Is it appropriate to ask my current supervisor for a reference?

I’ve been doing a lot of interviewing this past week, and I have more scheduled for next week. I’m just trying to maximize my success.