Your life is not worth the cost to stay.

Also I was able to get homeowners insurance to cover the outside of my section of the building in case something happens. 

There are not too many people who are a nerd like me and would like to build a map and list of all the people who signed up for Life Alert recently! 

Seems to me that if your sales contract says that you are to receive the security deposit then you are entitled to an amount equal to what the leases state, if they say that an amount was collected and he did not collect then shame on him, if the leases say that $0 security deposit was collected then shame on you for not catching it move on with life.

But I keep hearing people telling me not to rent out a property with a swimming pool because of insurance/liability issues.If I intend to insure it fully, am I still gonna run into problems?

Interesting transactions are the story of my life.  

He recommends to purchase more liability insurance."

You are paying them a monthly fee & insurance so they are more opt to consider you pay them to hang your license while learning the ropes.  

Hey BPCurious to hear what companies people have their rental property insurance through in NYC and what the rates are.

I dont know this for fact, but at the very least I would think the new GC would have to supply insurance info and licensure to L&I before anything is swapped.