Peter,Although the cost is small for the endorsement (or $0), you are impacting your coverage. 

I would just comprehensively screen him (credit, criminal, evictions, employment verification, social media check, google search) and if everything checks out, approve him.

Its bundled in with the Home insurance.Since I just started my loan, the bulk of the value of assets (liability coverage) I don't even own, I don't have much equity in my property yet but we count the total value of the property.Will that be worth going after if I get sued?

Any addition whether you extend out or go up needs to meet setbacks, lot coverage, FAR in some cases.  

Make sure you're protected well with $500,000 (or $1M) liability on the properties, make sure they're Replacement Cost (versus "ACV" or depreciated value), make sure you've got some personal property (appliances, window coverings, etc.) coverage, I always add in some 'additional replacement cost' as well as inflation guard too. 

There are a few that would benefit from either a wider angle or multiple photos ensuring full coverage.

There are lots of factors to consider when investing out of state - insurance, coverages, and rules vary from state to state.

When you buy a foreclosure on court house steps (not an REO) do you immediately call insurance agent for coverage?

When you work with banks, they generally write loans that have a proper debt coverage ratio.   

It is used to calculate the debt service coverage ratio.