Unless there's a VERY unusual situation, anybody wanting to sell just lists their home with a real estate agent.  

Is it unusual for landlords to buy with cash?

I have properties that would rent traditionally for $700-1000 a month, it's not unusual to pull in 3-4X that in a typical month, even 2x that in low/offseason.

I don't know what the experience level is of your loan officer, but it sounds unusual for them to call an agent to ask about an ARV?

That's not unusual.

The initial open house seemed to have about unusual turnout.  

Also, a seasoned co-op listing agent will know how to present buyers that have unusual income streams, are self employed, are maybe trying to time a sale and purchase, or are doing gifting, co-purchasing, or need guarantors, etc.

There can be generally a week or two lag between a closing on a REO, and the bank actually executing and recording the deed...not that unusual.  

Nothing unusual about that.

Definitely sounds like something systemic is causing these units to go down as that is a very unusual amount of needed replacements