After all, if the cap rate is higher than the interest rate, then I'm making profit on the bank's money. 

This way you have immediately created separation and should something terrible occur and you be found liable / negligent, your primary residence and bank account are more so protected.If you purchase the property in your name, it’s a personal asset.

Rent collection is via my bank account.

I’ve been working as an independent contractor physician since Nov 2015 and had two years of income tax returns and had to submit recent pay stubs and bank account statements to qualify for the FHA loan.  

You have to have it set up ahead of time at closing so that all of the proceeds sit in the bank account of a qualified intermediary until you close on the new purchase.

Hello BP,We are trying to work with Chase Bank on a short sale.

So just say out of the $xx required for closing, i have the money coming from Cash in the bank and the HELOC.It should be fine and if its not - you should reach out to another lender.

You're going to be hard pressed to find a bank that is going to give you a regular loan on a property that needs a lot of work. 

You’ll want to contact a tax advisor and a firm and bank who is experienced in setting this up.

CONVENTIONAL:A conventional loan allows you to put as low as 5% down and go up as high as you want, some banks may allow you to come even lower.