I may have posted about this before, but we used to run the children's programs in a former church. A fairly large program, we had well over 100 children from birth to 5th grade. For the nursery, all I can say is, it's so hard to run it and meet every parent's expectation. You seem to be going into this very eyes wide open and reasonable.
Honestly, my strongest concern was safety for the children and peace of mind for the parents. Background checks for the workers, multiple workers during each service, training, etc. Along with that, I didn't allow children younger than high school to volunteer or hang out if their parents were in for their scheduled day. And, I was really careful about allowing parents to wander in - understand that I mean a difference between "wandering in" and spending a bit of time or multiple days getting their child used to going to the nursery. Little ones like to escape, and they miss their parents, and if they see the door open, they'll run. When they see grown-ups coming and going, they expect to see their parents and get pretty sad.
So, that's my take on the safety aspect. From a leader's perspective, (and a mom's...)
We let the little ones watch tv. It was running in the corner. We used either a veggie tales dvd or a praise baby dvd so they were hearing good music and some bible stuff. Once they were around 2, they moved to the next room and were taught a bible story, colored, sang and got to play. Worked pretty good. Then, at age 3, they moved up again to a great program that is expensive but awesome, tailored to 3-4-preK's. It's video driven, has stations of coloring, blocks, etc, individual teacher time. Awesome program.
So, for your son, since you're looking for a place that will give him some bible stuff, I say go to their web sites, check what they have for his age group or starting at age 3, and invest your next few months getting him acquainted with the people who will be leading him.
About the food, take what he can eat. Kids need to snack, so for the hour of so he'll be there, they'll probably be given something. I'm sure there won't be a problem with them giving him his own snack. They're probably used to watching for allergies and stuff.
Security also can be addressed with a labeling system. Many churches have a computer system that will print labels for their back with their name, yours, allergies, etc. You have to have a matching label to pick him up.
All that said, you also have to find a church that will work for you, it would be hard to find one that has a great nursery but bad teaching or leadership.