Welcome aboard the RoadTrip America Forums!
Typically, the peak of fall foliage in the southern Appalachians (Tennessee and northern Alabama) occurs in early to mid November. This year, that would be roughly the week of the 8th to the 14th, although probably a week on either side of that would still be spectacular.
The basics of car rental were laid out in
this post, so check that and see if that answers your questions.
As for non-touristy things to do, you might want to have a read through
these lists of things to see in each state. Some are typical tourist attractions, some are definitely not.
My own preference for places to eat while on the road is to find a town with a population of about 3,000 to 5,000 and to drive along the main street downtown. There will usually be one or two local restaurants or diners. These are the places that rely on local repeat business rather than the one time customers that are the mainstay of the chain fast food joints out on the Interstate. They tend to offer a more local cuisine, friendlier service, and the chance to observe people in their 'native habitat'.
"Event"s is a pretty broad category, but probably your best bet is to stop at the welcome centers as you enter each state and see what flyers or pamphlets they have out. Or just keep your car radio tuned to the AM dial.
AZBuck