Do rates tend to be different if you're asking a teenager rather than a professional nanny or sitter?
Yes, a teenager will cost less than a trained, experienced nanny. Much of the money you are paying, in my view, is for 'peace of mind'. All the bits of paper a professional nanny will have, help give you as the parent 'peace of mind'.
I started babysitting as a teenager, and certainly didn't charge anywhere near what I do now. Back then I would often only be babysitting for a couple of hours, not for 4+ hours, and the children were often pre-school and school aged. Now nearly 20 years on, I tend to care for babies and toddlers.
When I was a teenage babysitter, the children would 9/10 times be in bed, asleep. These days, 9/10 times the children are awake and up and about - I take over the evening routine, so bathtime, story, evening feed, twilight feed etc.
Giving a babysitter a lift home these days I don't think is expected. I don't recall ever getting a lift home. As a teenager, I used to cycle to/from babysitting... until I learnt to drive. If you are going out to enjoy yourself - you may be consuming alcohol, and getting a taxi home... thus last thing you will want to do is drive your babysitter home!