@Alexander857 Most Airbnb hosts do not take the length of booking you are talking about. Airbnbs are primarily short-term rentals, not 6 months to 2 years. When homeowners rent for that long, they prefer to rent as a landlord/tenant arrangement, with a proper lease agreement, tenant providing references, work history, proper security deposit, etc.
And no, you most definitely can't declare an Airbnb as your residence without the host's permission- that could easily get you booted out, and would be incredibly disrespectful.
I'm not sure why you think that renting an Airbnb for 2 years would be cheaper than finding an apartment to rent, or even a room in a home that takes lodgers, which is different from being an Airbnb.