can a former president keep on using air force one?

Nope.  Only the sitting President flies in aircraft designated Air Force, Marine or Navy one.

Air Force One IS NOT a plane. It is the CALL SIGN used by any aircraft operated by the Air Force with the CURRENT President on board. The exact same plane files under a different call sign when the President is not on board.
Even if a former President is permitted to fly on the plane normally used for transporting the President, it wouldn't use the call sign Air Force One.

Nope.  Thats why trump had to leave when he did.  At 12:01 pm on Jan, 20th he was no longer authorized to use it either M1 or AF1.

Not for very long.  They are allowed to fly home on their last day of office, and if they are still President when the airplane takes off, they are allowed to stay on the airplane until it lands in their home state, even if they are no longer President because the next President took office while it was in the air.  However, after that, they normally can't use it for themselves.

They can fly on it as a guest of a subsequent President if they are going to the same place.  For example, when Clinton was President, former Presidents flew with him on Air Force One to get to a funeral, and slept in the physician's office on the plane (because it was the only room with beds that weren't reserved for the Presidents and First Lady), and the physician later wrote a memoir in that began by saying that she didn't sleep with the President (remember, this was a woman who worked for Bill Clinton for several years), but she did "sleep with the ex-Presidents", before explaining what she meant.

the aircraft has been withdrawn and returned to normal government service