Can you suggest an insurance company and contacts for our rental houses?

I'd say just start your search with all 2-4 unit properties, and when you find one where the numbers make sense and it checks your other boxes (somewhere you actually want to live and house hack), then it probably makes sense. 

I've been managing for 15 years and have helped a couple owners change/expand their portfolio. 

Educate yourself on how to house hack.

My favorite was a hoarder house full of trash that took me six months to turn around, but it turned into a killer deal that earned me a 600% return.

One of my friend happens to be a RE agent, landlord and a property manager himself and he seems to feel that as long as she pays rent on time and does not create nuisance, not to worry much and just keep do a quarterly property inspection.

Goal here is to use the VA's 0% down on a multiplex and rent out the unit I'm living in after 12m.
The mental gymnastics I'm going through is how exactly that would work without committing fraud.
Can I refinance m...

There’s normally action items that can be implemented into your management process that are more effective. 

I am back to getting the house rehabbed. 

If you think you can manage a mortgage, taxes, insurance and the upkeep of a home while paying your student loans then buying is not  bad idea but if you think you will overstretch yourself renting is nto bad either.