Our Ayi comes in one afternoon a week for 4 hours. We pay 20rmb/hr.
We live in a high end development. In the city you might be able to pay less for an hourly rate.
Regards cooking. Unless you are really into local food it may not be a good idea. Don't expect the ayi to learn anything new, although some people have been lucky.
Don't leave out cash or valuables, it can only lead to misunderstandings, especially if your wife or other household members are Chinese. I have lost count of the times that something was perceived as stolen, only to turn up a couple of months later.
Live in ayi, no idea about the rates, but they may have a child or other family member come to stay on occasion. They will all sleep in the same bed, but all eat your food. You need to be OK with this. Even with a live out ayi, a child might call in on the way home from school and wait for mum to finish, and join the family meal.
Contracts - no need. An ayi will usually do all task that are asked and will be paid the same hourly rate. The only difference would be childminding. Contracts don't mean anything anyway. For an hourly rate ayi, you need to negotiate how much cleaning is to be done, and how many hours it should take.
You need to monitor the ayi's work as some will steal time.
If they are going to look after kids, it is better to get personal references from people she has childminded for in the past.
Always get a photocopy of their household ID, and keep it safe. If there is any problem you will need this to identify them. If you live in a managed residential area, check with the management if the ayi needs to register with them also, this is an extra safeguard for you.