Listed as a licensed rooming house. Does the license come with it?

The thing I'd want written down before anything else is what the municipality calls this use. Rooming house, boarding house, lodging house, congregate living, single room occupancy. The words matter because the license, the inspection cycle, and the occupancy limits attach to a defined use, and definitions vary by state and by city inside a state. Ask the zoning office which category the property sits in and get the answer by email, not on a phone call.

On grandfathering, legal nonconforming status generally survives as long as the use continues without a long interruption, but what counts as abandonment and what counts as an expansion are set locally, so you'd want someone licensed to read your specific ordinance. The failure mode I've seen is a property sitting mostly vacant for a year during a sale, and the city taking the position that the use lapsed.

quill, patience costs you nothing here. If it's a real deal in April it's a real deal in June.

I'll check the math since that's the part I'm good at and the part I over-do.

3,850 gross if full. Take 620 utilities, 180 cleaning, and you're at 3,050 before anything else. Now the stuff the rent roll doesn't show: taxes and insurance on a rooming house, and insurance is the one that surprises people, because a lot of carriers price this as a different animal than a single family rental and some won't write it at all. Then maintenance, and shared kitchens and shared baths get used four times as hard as private ones. Then vacancy, and room vacancy is choppier than unit vacancy, one room empty is 17% of your gross gone.

At 340k with financing you can actually get, I'd want to know the debt number before saying whether 3,050 minus all that clears. Run it at 85% occupancy, not 100. Five rooms filled, 3,200 gross, and see how it looks then.

Something worth adding here is that you're buying a job. Six adults sharing one kitchen means you or somebody you pay is settling disputes about the fridge. That's a person, weekly, forever.

plumb is right about the job and hollow is right about the 500, so I'll take the zoning piece.

When you call, don't ask "is a rooming house allowed here." Ask three separate questions, each in writing. What is the zoning district for this parcel. Is the operation of rented sleeping rooms to unrelated individuals a permitted use, a conditional use, or not listed in that district. Does the city have a separate rooming house or lodging license, and if so, is it issued to the property or to the operator.

That last one decides your transfer question. Licenses issued to an operator generally don't ride along with the deed, and you apply new, which means a fresh inspection against current code rather than whatever code the building was inspected under in 2004. That fresh inspection is where hardwired interconnected smoke detection, egress windows in basement rooms, and door hardware show up as line items. It varies by jurisdiction, so confirm with the office that issues the license.

I'd also pull the property card and check whether the assessor has it as a single family. If the city's own records disagree with each other, that's worth knowing before you own it.

Reading this as somebody with nothing bought yet, the thing that stuck with me is that the agent's confident "it just transfers" is the only source for the most expensive assumption in the whole deal. That would scare me more than the utility number.