You'll be surprised how big they are by fall. You won't be able to fit four under your light, but it can supplement whatever other light you might have. I have a 400W metal halide for my tropical hibiscus and I have kept various bananas next to that and a west window over the winter. They like the light and heat and keep growing, although more slowly. The spider mites love them though. Adding a humdifier helped but I still need to spray or wipe them down periodically and they usually look a bit shabby by spring. After they go outside they get happy again.

I have not tried letting them go dormant over the winter. I don't have a good cool, dark place to store them.

In southern middle Tennessee when would be best to dig up my 7 foot bannana tree for winter and when to cut off pups from parent plant

Dig them once your average temps get in to the 60's or at least a few weeks before expected first frost ... Cut pups when they are about 18" and its warm enough to get some growth before they go dormant just make sure you get a few roots attached to them water sparingly till they start putting out leaves.