A few mistakes/ suggestions. Speak to a lender, it doesn't hurt to ask a knowledgeable one.
1.) Conventional financing down payment goes up if it is a small multifamily property. 15% I believe.
2.) FHA limits go up depending on the amount of units so it might still qualify.
3.) the tax bill reduction could be temporary. Perhaps for a veteran credit or something. Ask seller.
4.) I would personally be careful of an agent with two jobs that require a lot of time and practice to do well.
5.) Such a high number of days on market EASILY calls for negotiation of price. In my market depending on the seller and listing agent, I wouldve called for a 18k price redux and have seller pay 7k or so in Buyer's Closing costs. I would try an oral offer first with good reasoning behind the reduction. (below market rents, corona, economy, etc)
6.) There was no mention of who pays what utilities. Since the cash flow potential initially is so low, this could make or break the deal.
7.) You are correct on thinking about current market rent. The current rents play a role in your decision, but market rents should also play a large role. Of course depending on the condition of all the units.
8.) Ask listing agent for seller reasoning. It could be anything. retirement, tired of being a landlord, inheritance, just wants cash, etc. you never know but it can be used for negotiations.
9.) Depending on your area, buying a property that doesn't cash flow while you live in it is completely fine. Especially if the negative cash flow is temporary due to lower than market rents. The purpose of a house hack is to have other people pay all or a portion of your mortgage. Since you did the math and figured you would live in an $800+ unit for a bit over $200, all while controlling a $400k asset with tax benefits means it still accomplishes the house hacking goal.