She was a part time maid, making about $15,000 gross per year. 2 months into a 12 month contract with CMHA, they conduct a "financial review" on my tenant and decide, before talking to her, that she makes a sufficient amount of money to pay $687 per month and they reduced their portion to $367 per month, down from $966.

The area you've drawn here contains portions of Cleveland, East Cleveland, Cleveland Heights, Euclid, and South Euclid (touching on zips 44106, 44112, 44118, 44121, and 44117) and seems far from sufficiently homogeneous to make it one single area as you've drawn it (assuming price is your only driver).

Are adjacent occupied (and therefore heated) units sometimes sufficient to keep pipes in common walls warm?

Same thing I always do:Buy an asset that cash flowsBuy with long term (7 year term plus, 25-30 amortization) and low leverage (75% loan to value or less) debt.Have sufficient cash reserves to handle at least 6 months of PITI per property

I have multiple questions...1st) is it legal for the property management company to open an account in my husbands name without authorization and is it legal to use a blank amendment as sufficient documentation to do so?  

My only advice here would be to make sure you have access to sufficient working capital should a bigger ticket item need repair or replacement before you are able to set aside enough from monthly cash flow. 

There are plenty of options - you can add federal search for extra money but most tenants are local and just your state is sufficient.

Again I'd only do it if I'd given the agent sufficient opportunity to respond.  

Is this sufficient enough?

@Kevin Agunbiade When buying 3-4 unit MF properties using an FHA loan, you'll want to make certain the property passes the Self Sufficiency Test, which is that 75% of the market rent for the 2-3 units you will NOT occupy will be sufficient to pay for the mortgage payment.