If you have equity and decent credit, a conventional Fannie Mae HomeStyle (or the Freddie Mac version) would likely be the better option instead of an FHA 203k loan (which will require a 3rd party HUD consultant to oversee the deal in addition to having the contractor involved). 

I've read BiggerPockets' Real Estate Investing book and am particularly interested in the house hacking strategy, as I'd like to move out of my current living situation.Our main dilemma is choosing between a single-family home (renting out one room to a close friend) or a multifamily property like a duplex or triplex.

How many mortgage lenders have you spoken with to get qualified and discuss allowable down payment options?

We walk it, get the reno budget in 10 min, make the offer, close.

But I think the better option is tenant pay for it, that way they will know it may go against them for not paying rent..

I have lenders that can fund in just a few days and are willing to finance up to 90% of the purchase price and up to 100% of the rehab budget, even for first time investors.

Eg, i have a friend/client who determines it based on income vs PITI.

HELOCs are definitely a good option for financing BRRRRs.

What if she lies and claims to have owned a home, or uses a friend's address instead of the rental address?"

It's much cheaper than Buildium and offers similar tenant screening options.