As a pre-qualification is marginal at best to see if you can really afford a home.  

Know your ceiling offer before hand and don't ask for a pre-pay unless it is demanded or absolutely needed to close.

From my research, VRBO tends to have many more listings at "resort" type areas (think beach areas and ski areas) where as AirBnB has the larger part of "urban" listings.  

We pay them 10% APR in monthly payments.

I have locked in the rate with them, and they've given me two options, both 30-year fixed:3.375% (3.42 APR) OR 3.5% (3.5 APR) with 0.5% credit.The 3.375 is great but the hangup here is that we would like to refinance the house in May, when we will be able to take other income into consideration and hopefully be able to get some money out of the house, as we are currently putting down 40%, the minimum allowed by the bank.

I am now ready to buy and house hack a multi-plex.I have $20k for a down payment for a FHA style loan (I'd only put down 3.5%) at ~3.8% APR. 

This could range from using a pre-existing power pole, to needing multiple poles installed for you.

I would not accept or even negotiate any offers until I saw a pre-approval.

$60k at what APR, how many years left on the note?

If you know you will be having a formal inspection period, and you know you will be able to back out because of inspections, then don't worry so much about a pre-offer inspection.