Can a business place a liability sign in their store after being sued?

Yes. Under ordinary circumstances it is permissible

We're basically lost on how to make sure someone is able to be in charge and take over everything without hassle.

No. You really should see a local Cleveland attorney. Many do wills and estate planning.

Will the accusation be in a background check?

Only convictions turn up on b/ground checks.

Can I file a motion to vacate judgment based on the fact that the tenant could have prevented the damage if reported?

The ans is that it probably will not fly. My aunt always said, "You do not ask you do not get." Accordingly, my philosophy

Does my lawyer need to be with me at the Oath Ceremony?

No that is not necessary................................sometimes an atty likes to be there

Never stop appealing unemployment benefits while in the administrative law system (without going to court). Each time is another opportunity to win

How can I get this to stop? I keep filing HIPAA Violations to the OCR, per incident, and the DA won't grant a Restraining Order.

If anyone is in real danger you need to call family services

How do I go about getting money back from an ex roommate that owes me more than $1200?

You cannot get emotional damages.....you can sue for what he has cost you on small claims

Since I cannot afford to pay a lawyer, how do I find an attorney to represent me during my disability hearing?

Look, take the time to search for a SS atty here on AVVO. If you cannot find one call a local bar ass'n

What are the legal or financial implications in the absence of any written agreement regarding compensation?

You have unfortunately not provide enough information here in which to answer!