Hi OP,
I know you did not ask this, but please also carefully consider non-monetary costs of the program, such having a young adult live in our house. Someone, who may have never lived on their own before, someone who may require a lot of hand-holding, someone whom you would be integrating into your family, and someone with whom you won't have a simple employer/employee relationship. Don't get me wrong, sometimes you get a lot in return. Anyway, if all of this sounds good to you and if you are still interested, here's my take on your questions.
A good resource what you may have already found if you did any research on your own is this site:
https://aupairmom.com/
If you have a child younger than 2yo (even if you don't plan on having the AP take care of this child), you will need an Infant Qualified (IQ) AP. This means that (at least on paper) an IQ AP took care of young children for a certain number of hours. All agencies distinguish IQ from non-IQ au pairs. All other distinctions are not regulated. For example, I believe that APA has extraordinaire au pairs, while CC does not make this distinction. You should spend some time googling what each agency has and compare definition. For example, I don't believe that all extraordinaires are IQ. The requirements are simply different.
IMHO, agency does not matter much. What matters is that you find the right candidate. The only caveat is that if you go with a smaller agency, your rematch pool may be smaller, should things go wrong with your au pair. The three big ones are all fine.
As for the questions to ask the candidates, this is probably family specific. The questions about childcare will depend of the age of your children and the tasks for your au pair. For example, there is a big difference between choosing an au pair to take care of a 1yo in an urban setting, where she does not have to drive vs. finding an au pair for help tweens with their homework and drive them to their activities. Also, please spend some time thinking about what is important to you in a roommate? If you have dietary restrictions, talk about them? If you are super neat and cannot tolerate crumbs, talk about that. Are you a sporty family or more chill? Overall, be honest in the matching process; withholding information only gets you in rematch and the latter is stressful.
Good luck!