I want to create a new checking account to keep all my house income expenses separate from personal expenses.

Can a person own two homes with two VA loans and refinance one of the homes  into a conventional loan freeing up some of the entitlement which would enable you to buy a 3rd home under the VA loan?

Personally, I would be hesitant to jump into a deal when the existing partners are cash-strapped.

I tend to agree with you, but that is my perspective.Let's say you are trying to raise money from other people: banks, private lenders or investors.  

I personally would reach out to your real estate attorney.

Without bank approval?

I have personally never heard of the county having any say .. other than I do get calls from (state of Colorado) Tax collector after I purchase something and they want to know why we paid less than market value.. but they contact after the fact..

I have used this strategy personally more that 10 times and helped many clients doing it.

Regular reconciliation of accounts and maintaining a clear separation between personal and business finances is crucial.

Why is it asking for personal info?