Many families have Non-Jewish au pairs in London. This is because the mothers are working. Is there a specific book we can read about the laws regarding what these girls can and cannot do? Especially with regard to cooking for children, can they use microwaves to heat up ready cooked foods?

I cannot recommend a specific book, though I'm sure there are some. A google search with the key words Halacha Bishul Nochri will give you several excellent summaries of these Halachot. The most basic rules are that the prohibition requires three conditions: 1. The food was not fit to be eaten prior to the cooking 2. The food is fit to be served as a dish at a formal meal 3. The food was cooked entirely by a Nochri In the case of the microwave since the food is precooked, it can be rewarmed by a non Jew.