I responded to her saying that we cannot offer any incentives for her and would like for her to honor our current lease agreement, and she replied by asking if she'd lose her deposit if she leaves.

There are some other requirements around language in the company's operating agreement, but like the self-certification, that's likely something that could be done at this stage, too.  

Most buyers offer quotes at no charge.If you agree on pricing and decide to move forward, you will sign a sale agreement and there will be further due diligence which includes:Title report Borrower(s) credit reportProperty valuation reportReview of property taxes, HOA, or other potential amounts dueProof of property insurancePay history reviewPossible Borrower interviewSome buyers absorb underwriting and closing costs, others will attempt to negotiate them.

And just to reiterate, they are currently on a month-to-month leasing agreement from the previous owner.

Reach out to a local attorney and ask them about setting up a joint venture agreement for you. 

Have a RE atty draft an agreement since both parties sound amicable.  

Review their management agreement.

As long as they were closed on prior to Feb. 15th and can be proven utilized as rental properties via income and lease agreements the lender should not care how they were acquired.

If you are unsure about the investor paying you then yes write up some type of formal agreement.

I'm currently renting out one floor for $1,000 / month with an agreement to raise rent to $1,100 at the start of the year.