1. Per Airbnb, they insure material damages as well as personal injuries. Make sure to read up on so you're well prepared. It would be EXTREMELY unlucky if something were to happen with your first guests since I've hosted many without a hitch. If there are any material damages, make sure everything is properly documented because Airbnb will ask for the granular evidence.
2. No, the only thing you pay Airbnb is the 3% fee that's charged to hosts. It's taken out of your payout.
3. "Averagely Clean" is definitely NOT OK. Being both a guest and host myself, when I see pictures, I expect the space to be exactly as it is minus some furniture rearrangements which happens quite often. Your listing looks absolutely stunning and definitely raises expectations. If the space is not as advertised or lives up to expectations, then expect to get some low ratings. If you have time, hire a cleaner ASAP, it's worth it.
4. It varies from host to host but definitely use your better judgement. I provide a plethora of items from coffee and tea, to virgin olive oil and spices for cooking. The personal gifts I leave are either a bottle of wine for couples, beers for groups of friends or a gift certificate for a local ice cream store for families with young ones. This one will be something you'll have to figure out yourself.