Hi Rory,
1.) You are correct, Airbnb do pass on rental income information to HMRC as a requirement.
However, it is also your own personal responsibility to inform HMRC of any rental business income via the Self-Assessment Tax Return.
This is done within the SA105 property page if your profits exceed £2,500 after any deductions are taken, with profits between £1,000 and £2,500 notified to PAYE.
2.) Depending on certain criteria, rent a room relief may apply.
Please follow the attached guidance for more information:
Rent a room in your home
3&4.) Within the SA105 page, there shall be boxes to disclose rental income and expenses depending on the type of expense incurred, to which the calculation shall only produce a tax liability if a profit is made and your personal allowance has been exceeded.
Thank you.