If it needs mowing, keep mowing. :-) If it stops, stop. :-)

It sounds kind of flippant, but it's true. If you made me guess, I'd almost guarantee growth will stop. In December. Light levels will be very low, temperatures will go more than low enough to stop growth from what I see on the climate charts, and that'll do it all by itself.

When growth ceases (it may continue, just very, very slowly), we generally recommend feeding with around 1 pound of nitrogen per thousand square feet, so apply any high-nitrogen, low everything else, fertilizer at bag rate before about 0.25" to 0.50" of rain or irrigation. That'll supply nitrogen to turn into carbohydrates for energy supply through spring.

Growth should resume in late March or early April most years. A first year lawn will usually be late coming back just because it's very young, although fescues do mature quickly.

Hold feeding until Memorial Day (although as far south as you are, I might be inclined to feed about a week after the spring growth flush stops, which is more likely to be May 10th-May 20th since you'll shift just a bit from the norm).

Every lawn differs. Mine tends to "stop," in the sense that most of it doesn't require a mow, but the southern sections and areas near the house and garden do grow at modest rates. The entire lawn still grows even in January, just really, really slowly.