And the bad new is, if you stay in the property you have to pay the property debt. 

The thing that people miss is that although having a debt free real estate portfolio would certainly be nice, the vast majority of large scale investors (yes even the millionaire ones), do not have debt free assets. 

Your looking at a 7% cap, it's an alright cash investment, but it wont float with debt services.

I have about $22,000 in student loan debt.

Yeah the issue is the "re-entitlement," for your father because once the VA loan is paid off there is a process probably through the Arizona VA office to restore that entitlement so the VA program is once again available for his purchase.So depending on his close of escrow date for this new home and when it is or how flexible the seller is then using a refi to conventional and VA for purchase would be possible even with a couple hurdles.I think that is the most efficient path too since VA rates are generally lower than conventional.

A avoid personal debt 2.

I'd like to get an FHA loan to do a cash-out refi and use the money for home improvements, some minor debt pay down (mostly to raise credit scores) a cushion for starting my real estate career, and ultimately buy a new house and convert the current one to a rental.

I rarely have DSTs available with that much debt. 

Paying down debt (student loans if any) and working on credit will also be helpful in the future.

The only thing that makes my numbers work is no debt service.