Rate is commensurate with their experience. And at those ages, you’ll want someone with experience. I’d say $25/hr and she should have 2+ years experience working as a nanny.
Yes they can do laundry but I wouldn’t go overboard. I typically had my nanny move laundry from washer to dryer or toss in a new load, but I did folding/out it away.
Call her references and get them talking. Ask about her dependability, her attitude, her helpfulness etc etc.
Nanny should work in your home. That’s where your kids toys and beds and stuff is! Why would she take them to her house? Unless she’s running an in home daycare or something?