Helmet laws exist almost everywhere, and in most countries they're mandatory for both rider and passenger, though enforcement varies from strict to theoretical in some tourist areas. Ride as if enforcement were strict anyway: beyond fines, helmetless riding is the difference between a scrape and a life-changing injury, and scooter crashes are among the most common serious tourist accidents in holiday destinations. Rental shops provide helmets, but quality ranges from decent to decorative, so check the fit and condition, and consider that flimsy helmets protect paperwork more than skulls.
Insurance is where renters get surprised. Many cheap scooter rentals include little or no meaningful coverage; what's bundled is often just basic third-party liability required by law, sometimes not even that, and damage to the scooter itself frequently falls entirely on you.
The bigger trap is your own travel insurance: most policies only cover riding if you're properly licensed for that vehicle category at home, and many exclude motorcycles or engines above a certain size altogether.