If my parents co-sign on my mortgage, would they be able to deduct mortgage interest on their taxes next year?
Probably not. The interest paid is reported on a form 1098 and it is reported under the social security number of the primary borrowers.

Why is my old HELOC now considered as "Cash out" if I want to refi and consolidate my 1st and 2nd. Does not make sense.
If you didnt take the 2nd mortgage at time of purchase but got it later and pulled "cash out", that's why Fannie Mae, Freddie Mac consider it cash out.FHA considers it cash out if you havent used it in the last 12 months.

What is the minimum credit score requirement for a USDA Loan?
Hello,The RD program doesnt have a minimum, but most banks and lenders require a 620 or higher fico score. I do have a source that goes down to 580, but the underwriting is much tougher.What is your situation?Thanks,Roger

Main residency and rental home, refinance?
You would get a better rate if you refinanced your primary residence and used it to pay off the mortgage on your rental. It would improve your rental's cash flow as well. You sould be able to write off the mortgage interest on your taxes. As always, consult your CPA.I would look at a conventional loan...