I asked her to do the basic cleaning and buy the food from the maket and prepare the dinner for us. It's better to make the rule clear when she is arrive, of course if her job is not satisfy your requirement, you can talk to her to maje the adjustment or even terminate her (I don't think there is any 通知期 is required.) BTW, you have to buy the insurance for her.
I pay her every week, but once I decide to hire her in a long run, I agree with her as a fixed monthly salary , it is an agreement between she and yourself.
I will give her 300 - 500 for her weekly marketing, you better tell her your budget per day, and ask her to mark down the items and keep the bill if possible.