Please tell us what kind of turf seed you are planting. I assume you are using TTTF. This is the best choice since it will blend with your existing lawn, and can tolerate both full sun and moderate shade. It is also the best cool season grass for the transition zone where you live. KBG in Tennessee is possible, but it's an uphill struggle. Also if you do go with KBG there are some cultivars that do better in your area, and I can almost guarantee you won't find any of them in a big box store or bag put out by Scotts. Check the NTEP trials to see which ones perform best in your region if you want to go that route.

Unless you are seeding zoysia or bermuda grass, then EARLY FALL IS ALWAYS THE BEST TIME TO SEED. The next best time is mid fall. If you wait until late fall then you don't have a chance to fill in any thin spots where you didn't get enough grass seed the first time. Spring is the second worst time of year to seed with summer being the worst. Even winter can be an better than spring or summer under certain circumstances.

If you do a dormant seeding, any fall/early winter fertilizing you do will be for the existing grass, not the seed you're putting down. The new seed won't make use of any fertilizer until some time next spring. If you want to give your existing grass a boost to keep it green later and give it a boost in the early spring (maybe keep it green all winter), you want to fertilize with 1 lb of actual N per 1000 sq ft after the top growth has stopped, but while the grass is still green. In the Chicago area, that's probably now. You can fertilize next May as usual in either case.

Compost should be added during cooler parts of the year this is a good time to fertilze also. In fall do a winterizer type fert. So it stores up those nutrients over winter and gets a better start in spring. Art