I don't think its bad that she still sleeps with it. At this point its probably just habit. I would let her keep sleeping with it if she wants.
Typically I would charge less for overnight as the kids will be sleeping so you aren't doing much. Some parents might prefer to use a flat rate instead of per hour as well. Ultimately its up to both the sitter and the parents to find a price they both... more
I don't think its too much! If a parent asked for my home address and a copy of my ID I wouldn't think it was too much. As you said your trusting them with your child.
I would ask for a walk through of a typical day, what my responsibilities would be (am I cooking, doing laundry, etc.), rules for electronics, how they would like me to discipline a child if needed, and I would ask for emergency contacts.
The Care.com Community is an advice-sharing network for parents and caregivers.