The downfall to this, is YOU are now the bank, and you must complete, pay for, handle legal representation of, the foreclosure sale itself, should you choose to go this route.Disclaimer statement-- My experiences, in Illinois only...

Can I legally "threaten" eviction?

If I can (Legally, Morally, and Ethically) profit while helping people stay in their homes, or helping them get a fresh start, I will do my best to be active in this area.  

MUCHO - it’s a SCAM - Legal yes Ethical NO!!!

You would do it all at one place: purchase, legal documents and they same people will also take care of your rentals.

I only lucked up with the deal because a friend was selling their deceased grandmother's house and they had to close in a short amount of time because of legal dispute with another relative over the property.

I am not sure nor am this is a legal advise.

Has no one given the tenant a legal notice to "Pay Rent or Quit" (or the equivalent for your jurisdiction)? 

Multiple pulls in a 2 week time period is usually counted as one pull as the algorithms know you are rate shopping.If you get pulls going on a few months each time you try to locate a property to buy then it can affect your score.If you know your score is high say above 740 middle score then you typically qualify for the best rates anyway and do not need credit pulled in the beginning.No legal advice given.  

If they have  a personal guarantee from you and you are not insolvent then I do not see that happening.They know you have assets and income and will go after you rather than taking a loss.The 20k is usually a promissory note where the bank agrees to release the collateral for XX and then you keep paying the difference.The bank might require you to secure the promissory note with one of your other properties that has equity to attach to until it is paid off.If you are paying 20k it will still cost you money but you will not own the property anymore or deal with tenants in a crummy area etc.No legal advice given.