It is certainly appropriate for you to require verification and if the person is pushing back, move on.The one with the woman contacting you in behalf of her son, that's not unusual for an initial inquiry but at this point, tell her you don't rent through third parties and he needs to contact you directly.

@Tim Bee usually I am trying to find buy and hold deals that are returning 10%+My expenses are usually minimal - public electric, RE taxes (PHILA taxes aren’t super high), insurance.Tenants are responsible for the rest: water, landscaping, snow removal, utilities, etc.I invest in small multi family usually duplexes, so having the tenant responsible for those items is not unusual.

When it was all said and done, we figured it was easier if we deposited one check in the beginning.There are other cases where I got such requests, though unusual, but not a red flag in all cases.I thought post dated check were illegal or is that just my lovely state of MA again ?

Being stuck with unusuable property is the opposite of what I'm going for!

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.

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.