I now also offer limited service where I do the guest communications, marketing, and pricing. 

What is the best way to go about finding these property listings online before they go to the auctions?

I found an auction person, and I see listings online.

From there, I would like to consider a 1031 exchange in the future to acquire more units.My current property management company suggested that they could handle a mid sized apartment building but I would absolutely not consider them for it as I believe they have overextended themselves and communication is lacking.

Poor communicators, poor housekeeping skills, prescription med abuse, big dogs that they couldn't properly care for, damaging, etc.

I can provide him with an online log in so he can review the books from his office.

Online metrics can be good, but they wont paint the whole picture. 

The city wants to tear the property and surrounding properties down Zillow said it’s worth 38000The city offer me 13000.I could use some adviceHard to give advice with limited information, but as a general rule, the longer you wait and the further down the line their project is the more valuable your property will be to them.Zillow (and all automatic online) estimates are very unreliable, so don't base on that.

My business has access to AppFolio, but it doesn't seem to communicate with the STR side of things. 

I always cover my experience, the brokerages experience, and expectations with communication - 9 - 5, M-F, 24 hr turnaround during business hours, and the owner can reach out to me personally when the team isn't present.