Squiffy/Cloudberry, Mrs Recycle's list is pretty comprehensive. I have a few other questions to add, a few are based on my personal circumstances:
Why do you want to come to [where you live]?
Have you had sole charge of a baby/toddler?
Have you changed nappies before?
[List one example of your dcs' challenging behaviour, in my case my dd's refusal to get dressed for school], how would you encourage her to speed up?
Can you describe the types of activities you did with the children you looked after? Did you take them out alone?
What references you able to provide? Are they in English? Also, contact telephone numbers for these references. Do they speak English?
Are your parents happy with your decision to become an Au Pair?
What do you plan to do after you finished au-pairing?
Do you have a UK bank account?
Have you had any first aid training?
What food do you like?
What food do you not like?
What is your favourite meal?
Do you have any allergies or health concerns?
What is your current level of English - conversational and written? Can you, for example, chat on the phone, understand simple instructions?
Do you intend to take English language lessons when in UK?
Do you have a boyfriend?