From what I can see this is not an option, the listing agent will reject this immediately.

Most property management companies will offer to place tenants for you for half of the first month's rent, so going forward if you decide you don't want to do this yourself that is one task you can hire out.If you want to know more, this is a great article that explains how to decline an application and has a sample rejection letter:https://www.apartments.com/rental-manager/resources/screenin...

A friend on the HOA board tipped me off that she's being foreclosed on when the attorney reached out to the HOA to see if there were any past due dues.I was able to tour the property and made an offer that she soundly rejected.

Include a copy of the property management agreement, any photos, estimates and most importantly the findings/rejection from your homeowners insurance.

I guess I'll make another offer, if they reject that, then wait for the 60 day mark and see what happens.

Next day she did this: send me the power company's rejection of discount for her electric bill when the house's thermostat is not smart one.

If you were put in a cash offer with the intention of using say a hard money lender then you will be exposed if the lender rejects the deal but usually there or no finance contingencies in an all-cash offer as opposed to an offer that state that you will be getting finance.

I let them know that any false statement(s) in the application may result in their rejection - or their eviction.

If they don't we reject them and move on to the next potential tenant. 

If he doesn’t meet ALL your requirements, and you apply these requirements to all tenants, and he doesn’t have a co-signer who does, then it seems you are well within your right to reject based on those facts.tenant screening is super important!