What document can I have her sign to ensure she does not ever try to sue me again. 

If they don’t meet one or more of those I’ll ask for additional documentation and or references and take another look as a whole.

I submitted the request and it was denied because my mortgage is owner occupied.

Our leases always state that any document signed prior to the date of the current document are null and void.

There are people watching the MLS 24-hours a day submitting dozens of offers.

-A preapproval happens when you submit all of your documents to a lender and your credit is pulled.

Continuing to look at deals and submit offers. 

That seems not to have happened here, but that doesn't represent an ethical breach.BTW, you can still submit a higher offer if the property hasn't sold, even if the agent says it's under agreement. 

On top of this, I'm considering purchasing another home in which underwriting (maybe 3-8mo from now) would probably want me to submit a current signed lease.I know I've committed the ultimate mistake by not having them sign any lease, but any advice as to what next steps should be would be appreciated.

Through the last couple of month, in addition to studying on the license I developed my knowledge of several real estate-related apps and software so when I am asking for an opportunity I would have something to offer as well, such as: Matterport, Inc (for making 3-D renderings of assets so that prospective buyers may take virtual tours)Repair Estimator Plus (for estimating the costs and expenses associated with each deal)Follow up boss (for centralizing communication)Cloud attract (for building landing pages)Wise agent (for email automation)LionDesk (for recording and embedding videos into emails and texts)Spacio (for digitizing open house sign-in forms) PalmAgent One (for estimating closing costs)Disclosures.io (for organizing and sharing disclosures)Dotloop (for signing offers and closing documents)Looking forward to hearing back from you.Best regards,Reza Rostamnezhad