Yes, it's okay to ask why but don't let it be the first question or so...and don't ask for specifics. Sometimes they may not want to share, I know with us we just said "it's an issue on both of our parts" when it's actually mostly my dh, but he would be mortified to have to talk about it in front of ANY one. KWIM?
Ask them to bring pictures! This is a great ice breaker and conversation starter also.
Oh, I don't know if I would ask to see the kids the first visit. First I wouldn't want my kids to get too excited if they know about the baby, and also I would want to give you my whole attention. They will be SO nervous, it makes it that much more so worrying about what your kids will say or do! LOL
Ask them EVERYthing and ANYthing!! Good luck!!
P.s. I have one person I know that got asked how her kids were doing in school and developmentally wise (like grades, when they could say the ABCs etc). She thought that was pretty innapropriate as it was asked the first visit and was asked to try to get an idea of her parenting, not just as a conversation. She may have been sensitive because her child has ADD and such so it takes him longer...but she said the emom was very "abrupt" with it. She (aparent) ended up telling the agency they were not a match the second the meeting was over.