Having been a professional for many years, I do have a few suggestions.
It sounds as if this aide may be very young. However this doesn't give reason to take advantage of anyone.
When you feel that she does know what you want, continue to have everything charted and signed each day.
As for your car, I would make sure that your auto insurance covers her. Also it is really very important for her to know that your car is to be driven only for your benefit , not for her to run around in.
She works for you! She has to know exactly what you expect of her, in order to do things your way. If you have a specific way you want the laundry done show her what you want. She cannot know unless she is told and or shown.
I did not know home health aides did house work. I was under the impression that that comes under the chore services heading.
If these are the things that she was hired to do insist that she do them the way you want them done. Just try to remember that it is hard to please a woman that is used to caring for her own clothes and home.
I would be the worst patient in the world in my own home. I can imagine how difficult it is for you to have to depend on someone else to wash your clothes and drive your car. Just keep telling her what you want. Then when she does something well feel free to tell her that you are pleased.
You will probably become very attached to this woman.