All you need to do is leave a couple of outfits, a package of the correct size diapers, a huge package of wipes, and a large can of formula at her house. Ask her each week if she needs more of anything. I had so many parents bring everything except the kitchen sink, one even brought 2 diaper bags, for a newborn...we put them in a cubby in another room because we didn't have room. We never opened them either.
Your diaper bag should have a couple of clean bottles in it, one of course will have the formula she is drinking while bringing her there and others for formula during the day. A binky, a couple of toys that are soft and small. Keep it simple. don't bombard her with everything your child might possibly want.
As for what to call her, ask her. She may just want you to call her by her name instead of a pet name. We called the kids babysitter when they were younger "Nana L" , as for her title, she is your child care provider.
It's a hard call what to say when someone is watching your child and they aren't licensed as a home child care provider. I would just call her a babysitter to anyone outside the family so someone doesn't turn her in for running an unlicensed child care business.