A few questions about the Jewish Hospital apartments

Hey guys, it's my first post out here so go easy on me.:)

We, a couple, just saw some apartments on the Jewish Hospital apartment buildings (hmmm is there a new name for them?) They were beautiful and I thought good for the price. I read a number of threads here and joined there facebook group, but I thought maybe I could run some questions to residents and others.

1) One building we are looking at is 480 St. Marks. It was called the Dr. Leon Lauria Memorial building I believe. I understand that the whole complex was a hospital, but I wonder if anyone knows what specifically that building was used for? I couldn't find anything in a long internet search on that name.

2) I saw a thread with a lot of posts stating that the buildings didn't have a/c. Our realtor told us the heating unit also functioned as a/c. Is that possible in any of the buildings, or should I ask her to revisit it. Anybody have built-in a/c?

3) I saw some posts about break-ins in the buildings but it didn't sound completely out of the ordinary. Seemed to be some issues with doors sticking open and some keys stolen in the past. Any comments on that?

4) I understand the neighborhood is very mixed and has some history. I saws some posts out here that the area even next to the Museum isn't as safe as I would imagine. Can that be true?

I've lived in NY for over 20 years and know the deal all over as far as safety is concerned. I saw someone posting about using pepper spray when running, and about someone watching a mugging in front of the museum. I'm looking for just a reasonable balance between reassurance and heads-up.

The S train does indeedd seem to work great. Any comments on using it or commuting in general at 5 in the morning?

Thansk so much for any replies.