Hi there
I posted a similar question a while back when I was interviewing FD carers... I will see if I can find the post.
Anyway IMO ask as many q's as you can - they understand, you are leaving your baby there!! I think it is more about how you ask the questions.
I would def ask about who is in the home, ask who lives there and who regularly visits. I think some FDC agencies ask carers to keep a log book.
I also asked questions like:
do you like to take kids on excursions? what sorts of things do you do? (ie do they drive/walk and to check that they are things Noah would like)
which other kids they have when your baby will be there - ages etc
how long these kids have been coming
how routined they are - ie do they have planned activities or go with the flow
ask to see where the babies sleep
how do they put babies to sleep
how do they feed babies
where do they chg nappies
does anyone in the house smoke
in what instances do they call to ask input e.g. before giving panadol
why they do FDC
then see how their views and attitudes and philosophies line up with yours.

i only visited my carer once buti took her refs home with me for DH to read and then dropped them back one evening - this also meant i met her hubby too which is good as he spends time at home with N is there.
I met 4 carers before I found the one i was looking for... i think it is good ot ask lots of questions and see how you gel with them and how aligned you are in your ways of doing things.

good luck - i hope it works out for you - I find FDC a great option!