Aside from the obvious of looking at Facebook marketplace for rental rates, does anyone have suggestions on the best way to determine what I should expect this home to rent for?

Based on what I determined during due diligence:The annual vacancy cost was >$3,500/Yr.Maintenance was >$300/Mo. or $3,600/Yr.The cost to make each of the units livable was about $15,000 each.There was no way to raise the rent even if the units were beautiful.

Should someone "running the numbers" of a multifamily property include management fees when determining NOI to determine cap rate?

So, basically, the Tenant forfeits his Security Deposit to the Landlord.You should seek legal advice, or at least review your State's Landlord and Tenant Laws and your Lease, to determine whether this procedure is appropriate in your State.I hope this helps you.

The lenders use it to determine eligibility so why shouldn't you?

It was determined it needs repairs and parts are on order. 

It is a numbers game and with drive, determination, and the right systems set up, you can certainly succeed in finding deals in any market.For motivated home seller leads, you should really invest in a good website with proper SEO so your buyers can also come to you.

Again how they calculate it and what they include as "Expenses" will determine how much you can borrow.

How were you able to determine that the boyfriend is staying over without staking the place and watching him come in and out

It seems like the tricky part is to determine what amount would you start your offer that would seem to be generous enough for them to consider / take / start of as a negotiation point.