Do you all entertain sellers who do not want to discuss anything about the condition of the property nor do they have any pictures of the property?

Given that the property is ideally located and other economic conditions are right, you are bound to receive regular flow of rental income.

I have rented garages for personal items, prohibit flammables, etc.

While I'd never play around with safety issues, people who rent well below market have to accept well below average conditions. 

It might make sense to search a little more west of Pilsen in Little Village or the Marshall Square area to find something in better condition at around the same price.

But in the case of having it fully managed by others, with a STR policy that requires $1M liability anyway, plus the management company's insurance, wouldn't most liability fall to them first as they're contracted to keep the property in suitable condition, then I'd still have pretty hefty coverage if something went beyond that?  

The house is in pretty good condition, though it's built 1950's, it's had lots of updates. 

I have had a local appraiser tell me he runs into this occasionally - when he does, he says he 'has to' appraise the home as a conventional home (probably discounted some for condition unless extensively remodeled).  

Have you checked the condition? 

We prohibit the use of fireplaces in our homes.