Owner shall cooperate with agent and any insurer in the making and delivery of all reports, notices, and other items required in connection with any of the insurance policies.Is this a common thing for property management companies to be listed on my insurance?

You just need to make sure that your property registered for PGW LCP (landlord cooperation program).

If he is a Realtor® then he needs to disclose to you the presence of a valid Exclusive Right to Sell, but more specifically ANY COOPERATION.It is NOT a guarantee that because it is listed that there is cooperation. 

Told the seller he needed to shortsale, he agreed, my shortsale specialist I networked with here said the lender is cooperative and we are at the point where they are waiting for my POF to send for decision...  

for 1000 SQF, 3 bedrooms, 1 bathroom, PRICE RANGE 30-70 .Looking to establish a local team, we will be happy to cooperate and receive informationstart with which areas to focus on the light of our requirements?

I have insurance through American Modern and Wayne cooperative.

But requires cooperation from the borrower. 

There are many other issues besides this one for this particular tenant (i.e. paying rent at almost midnight on the 5th every month, not cooperating, not being cleanly and damaging property, etc.). 

All tenants are cooperative and current. 

I don't know if they would cooperate or not.