Does it still fly from the fantail of USN ships while they are at sea?
As the current Naval Jack it’s flow from the bow of USN ships while they are in commission but not underway.
In port, the ensign (the US flag) is flown on the stern with the jack at the bow. When I was in (late 60's to early 70's), the jack was a field of 50 white stars on a blue field. It was changed to red and white stripes with a yellow snake and the words "Don't Tread On Me" in 2002.
More info on the jack: wikipedia article
No. The Navy Jack is flown only in port and on the bow; the National Colors are flown on the fantail. When the ship gets underway, the Jack and Colors are taken down and the Colors shifted and flown from the yardarm of the mainmast. When the ship returns to port and ties up, the process is reversed.