Offered at 125K or best offer.

Knock on all doors of homes that are in pre foreclosure and offer to help.  

I would want payments to be made between 1-3 days after you extend the offer to lease.

Do they offer Cash-For-Keys or Payment Plans?

Essentially, the cap rate is the proportion of Net Operating Income (NOI) to the property's value or selling price:Cap Rate = Net Operating Income (NOI)/Property ValueThis ratio offers a direct method to evaluate the yield a property generates in relation to its cost.For advanced real estate investors, integrating additional factors might prove beneficial:Vacancy rate: The duration the property remains vacant.Operating expenses percentage: Includes insurance, utilities, and maintenance costs (excludes mortgage payments, depreciation, or income taxes).The adjusted formula for net income, incorporating these considerations, is:Net Income=(100 − Operating Expenses %) ×(100 − Vacancy Rate %) × Gross Income

Here are my initial thoughts:-Making the offer contingent on seller showing me background check documents from their due diligence-Requesting for a walkthrough of the property after the offer is made, and reserving the right to pull the offer if the house is not maintained wellAre these ideas practical?

You can skip trace the addresses using a tool like propstream as mentioned, give them a call and ask them if they'd be interested in an all-cash offer on the property, don't get into the fact that they are behind on payments, just ask them if they can use cash fast.

She offered for us to take the property off their hands so it was one less thing they had worry about after their mother passing away.

I would love to know if there were a compliant way to offer shorter stays. 

Owners mistakenly ASSUME all PMCs offer the exact SAME SERVICES and PERFORM those services EXACTLY THE SAME WAY, so price is the only differentiator – so, they often select the first PMC they call or that calls them back!