A smart seller will have note, deed of trust/mortgage/etc. prepared by a local real estate attorney (yes, he/she may work with/at the title company) and be sure the security instrument is properly recorded in the land records. 

Its essentially in the longterm best interest of the property owner to ensure there is a non-compete clause in all leases; merely for the benefit of securing longterm relationships with the tenants.A diverse tenant mix can attract a wider audience and contribute to a more vibrant environment.

Tell them if they don't, you will take it out of their security deposit and they will have to replenish their deposit.

That's not really a full story so it's hard to say, but generally, if you don't feel secure or confident in the person you hired, you shouldn't have hired them.

Credit score can help you secure a great rate so make sure to get started on that if you aren't already.

I can tell you that you won't secure a REFI term longer than the term that is left on your lease. 

Section 8 tenants are another way to secure rent payment with government backing.The Midwest is a solid market for rent growth, cashflow, and decent appreciation.Look at a market like Lansing, MI.

Do nothing...the tenant isn't renting that area and has no right to dictate how you use it as long as it poses no security/safety risk to them. 

Can I use her security deposit to cover these legal fees I've incurred due to her not moving out?

While I'm not entirely discouraged, I feel like I've invested significant resources (LLC, website, domain) without securing a deal that generates cash flow.Any advice or guidance would be greatly appreciated.