In my place, the insurance require rental property insurance must also have primary residence insured with the same insurance company.

if something (accident, damage) happens to one of my rental properties, can the insurance deny coverage for the accident happened to my rental property, simply based on the fact that I do not live in my primary residence (also rented)?

my 2nd question: does insurance gave the mortgagor (bank) the list of all houses I have insured with the insurer or just send the mortgagor the coverage of the house related to that house only?