Specifically containment of liability risk so the rest of your wealth is not attacked based on an incident relating to the property held in the LLC.2.

The coroner came by and picked up the body, but they didn't have any further involvement so I assume there was some kind of crime attached to your incident.  

In case of any incident related to roof or something, can insurance company deny the claim stating the age stated was not correct or something?

Early Monday morning, a 24-year-old gang member was grazed in the face after someone in a passing car opened fire on him in the 2000 block of West Diversey, less than a half-mile west of Tuesday’s incident.

Get a copy of the police report for the OD.Any unathorized people in the unit staying there not on the lease..If so write up lease violation.Get a crime free / drug free addendum for all your renters.Give them a notice of lease violation, High traffic, meaning just that to many people at weird hours.If you smell or someone else smells pot it's a lease violation and write them up.Non-renewal at next renewal time with proper notice.Offer mutual lease termination, or say any further incidents you will file for cause. 

I can understand from your post that this can be a frustrating incident.

An old incident followed by years of reformed behavior may not be just cause to deny someone.As for the background checks themselves, I've yet to find the "one stop shop" where you can get an all inclusive history.

I think of this as similar to a personal homeowners policy in that it covers the building(s) on this specific property as well as some liability for things related to the operation of the property, like someone suing for an incident on the property.

YOu might be able to get emergency eviction hearing if police write up or have written up any incident reports on the property.. 

Any formal agreements you do, make sure the written language covers things like: preventing a  partner from leveraging their equity (and the property) on another property purchase outside the partnership, lawsuit protocol (i.e. if a partner becomes party to a lawsuit separate from property incident it triggers an immediate buyout or dissolution).