No, petrol will not include during the bike on rent in Auli. Only sufficient petrol will be provided to reach the nearest petrol pump just for a top-up. You will have to fill the fuel by yourself based on the distance you travel.
You can ride the bike as much as you want, provided you return the bike within the specified duration. Any other additional penalties due to the rider, such as not following traffic rules, should be paid by the rider.