Avoid any communication with this tenant that is not documented (like email).

where resentment tends to build in your relationships or are you on top of communications and fair in your dealings?

If I'm understanding the timing correctly you have nothing to worry about, and if all communication has been done through the Airbnb app, they can see she threatened you. 

I have a few specific questions and would greatly appreciate any advice or insights you can offer:Tenant Communication: What's the best way to introduce myself to the current tenants and inform them about the change in property ownership?

This would have ensured better communication and transparency. 

I can't believe how many owners go for months with no communication and no payments, and then they eventually find out the tenant moved away, and the rental is sitting empty.

Communication/transparency with both current and potential investors is paramount to gaining the trust of LP's.

I have spent the last 8 years co-managing a small remodeling LLC, and have an primary background in project management, client coordination and admin communications/support. 

We have a great relationship and great line of communication. 

Haven't communicated directly with tenants myself.