http://www.agtlaw.co.uk/nurburgring_insurance.html
You are using your vehicle outside of the terms of the policy, they will try to recover their loss should it be large enough to make it worth their while. I’ve made a successful circa £15k claim for a crash there but that was back in 2003 before the insurance companies were quite so wise. The person I refer to crashed and several other cars then proceeded to crash on the fluids spilt by his car.
Local ‘ring specialist hire places will be fine but the excess is expensive.
Get passenger rides – don’t be afraid to ask people in quick cars, often they’ll be more than happy to let you hop in, if you have one take a helmet – I wouldn’t let a stranger in the passenger seat of my car without one. Go to tiergarten http://www.am-tiergarten.de/ (book in advance by email if there is a big group of you) and have large amounts of steak and beer, you’ll have a blast.
PS. There is a bike hire place from memory so you can get a bike and ride round the outside of the circuit to get to some great viewing spots.