You can focus your EDDM by Carrier Route (CRRT) within the zip code.

You should be able to get a general liability policy for each property through another carrier.

If you're staying on the residential end of things, I would suggest contact your personal insurance carrier to start. 

The HVAC salescritter will probably try to talk you into replacing the whole thing, but you don't have to.The houses I have lived in and owned, in Missouri and Oklahoma, have had Lennox, Carrier, and Trane systems in them, and they have all seemed to work OK. 

@Isaac Pokojni & @Jonathan Arcay any agreement between buyer and seller does not have any impact on the insurance policy.The only parties the insurance carrier can pay are those listed parties on the policy.

I think one could get reasonable indication of a probable renewal by discovering if that Post Office has recently reduced its hours or is having the carrier pick up mail for the route at another location.

You need to speak with the insurance company directly to see exactly what their policy covers.Here's a good overview.I recommend you contact at least three different carriers to see the differences.

That is not a landlord decision but the decision of the insurance carrier. 

Theft from vacant homes is typically not covered on any carriers policy and the threshold where vandalism becomes theft can be vague to someone who does not do insurance every day. 

I'd love to sit down with someone in person but e-mail, phone call, text, on BP, carrier pigeon... etc. is fine with me.