The plug is called a Powerlet plug and is standard to the BMW. You can buy a short adapter for it to power your american style cords. The one on the starting motor is typicly used for the battery tender hookup. Mine also has one up on the top of the beak alongside the windshield/dash area.
The oil level is something that takes some getting used to. The next time you check there may be a shade more. Why??? I dunno but they do consume some oil. On a longish trip i carry a 500cc container and if it needs a top up i have my grade and brand.
If I still had every dollar I spent on motorbikes I would be a richer man but a poorer person.