What’s different when airbnb'ing in a boat?

First of, you should consider if any of your party can easily get seasick or motion sickness. If yes then a boat AirBnB will be a miserable time for that person.

Second, any boat will be a cramped quarter.

Those factors can be impact your staying experience. As for operating the boatwhile staying, I cannot see any AirBnB owner would allow that.

Houseboats and other liveaboard vessels are not uncommon on AirBnB, and they’re as varied if not more so than every other type of accommodation. For all the questions listed, ask the owner, but here’s a rough outline:

• Most liveaboards have basic cooking facilities. If you are self catering, expect everything to be smaller and more rudimentary than on dry land.
• Whether the owner is on the boat with you will depend on the lifestyle and choices of the owner just like any AirBnB, and should be made clear in the advert (if it isn’t, ask), but things like the engine room (assuming there is one) will almost certainly be securely locked down either way.
• They should tell you if you need to bring anything special (but there’s no harm in asking). There’s nothing standard you might be reasonably expected to “just know” that you’d need. One exception: if you are planning to pose for photos on the boat in a captain’s hat, you’ll most likely have to bring your own :-)

There are just a few additional things you should consider that are boat specific, especially for a sailboat in an open harbour:

• If the owner isn’t going to be around, check what happens in case of an emergency such as a mooring rope coming loose in a storm. There might be a harbour master or similar, in which case, you might want to make sure you get their number, but you’re very unlikely to need it.
• Check that it is hooked up for electricity and water (i.e. clean water in, waste water/sewage out). Most long-term moorings will have these facilities connected straight to the boat, and they’ll “just work” just like in a house, but in some locations it might not be the norm and some nautical types might be so used to, say, only having 4 hours electricity a day on evenings from a battery charged by solar panels, or managing a septic tank, that they might forget to specify this to us landlubbers. But this is unlikely and is the sort of thing AirBnBers would be quick to complain about.
• There might be additional little things to do compared to a normal house, for example a procedure to avoid damp such as not keeping more than a few windows open or keeping a dehumidifier running, but the owner should tell you about these if there are any in the normal introductory tour.

Apart from that, simply pay more attention that usual when the owner shows you around, particularly to securing the boat and the “man overboard” procedure (probably just a rubber ring somewhere, but remember where it is!). If it’s your first time on a boat (never thought I’d be on a boat), mention it in your introduction email, and don’t be afraid to ask questions.

In general, I really enjoy staying on boats. Do be prepared however to have much less space than usual, and for any weather to feel twice as dramatic and be much louder than it normally would.

The answer to all three of your questions is "It depends".
The only way you will get an answer is by asking the owner directly.
If it’s being offered on Airbnb, then my assumption is that it is being offered much the same as any holiday rental. In that sense, the answer to 1. can be inferred from if it is advertised as "whole property" or "private room". 2 will be at the discretion of the owner, and 3. is likely to depend on the opinions of the owner and any local legal/regulatory requirements.

As the boat is being advertised on Airbnb, my assumption would be that it is being offered in the capacity of accommodation that happens to float, rather than as a watercraft. Again, all the above is an assumption, you will need to contact the owner to know if that really is the case.

If you are interested in a holiday on a yacht that moves around, then there are many services out there that offer this. Look for terms like "Flotilla" and "Bareboat". There are packages both with you as the entire crew, or with an existing crew. It isn’t cheap, but it’s also not so expensive as to be for the "1%" only. It could certainly be a fun way to visit some mediterranean cities.