My question is shouldn't my closing agent (law firm) research/ verified and disclosed this information on the HUD statement?

Go to realtor.com find deals you like, scroll down and see "presented by" then call and verify they are the listing agent. 

In that case ( please verify this with a CPA) any unrealized capital gains go away when his heirs inherit the note he holds on the property at it's present day principle balance as their new basis. 

In this case, especially if you're getting a better price and your sure a fairly identical unit next door has them, I might buy them.Another thought though is that if you don't supply them and therefore charged less, you might get the tenant who wants to pay less and actually does not want to use "someone's old washer and dryer."

The properties and units are identical to each other, but the properties are totally different colors. 

But at the same time, I want trust but verify.

You have a business plan and you should be looking at your business monthly- Trust but verify the numbers and the data.

As mentioned above you have to do some tenant screening leg work (verify timely rent payments, call landlord references, etc) and run credit and background through one of the screening services.

How do I buy my first investment property as a 1099 when basically no banks will give a mortgage to a 1099 without at least two years of verified substantial income?

This isn't verified but gives me an idea.