Welcome TyThere is lots of info here on the site. 

If you were me, based on the given info, would you:                 A.

It was very difficult to get any info about the tenants before we purchased the property and soon after we purchased it the tenants in one house moved out.I realize this is a very small sample size to draw any conclusions from, but I guess I want to challenge the belief that it is better for the owner that the tenant not to know who he or she is.

So, I really appreciate the info and the advice.

Assuming it is a purchase mortgage, your lender is correct.The disconnect is probably from reading about refinances and/or old pre-recession info and/or reading that you can roll some of the closing costs into a higher interest rate (but not loan amount).

Do they want bio info or do I just stick to search criteria?

Can anyone give further info on how the rental and tear-down market is doing there?

Background information.  There is a very much vacant property in my town that no one has been to in years.  I looked up the owner it seems as if it's a little complicated.  Man and woman own it, however the woman pass...

All zoning info is up to you.

He is not on BP, but I can pass along his contact info if that is helpful to you.