Why are you living apart?Who left who and why?
Yes you are still married, you both need to do something about this stagnation.
Have you both been to see your pastor about this? If so what did he say?
BTW its not dating that is an affair, its having sex that is an affair. However until you have sorted out the marriage don't think about someone else. If he abandoned you and refuses to return, then you are free to end the marriage, but you must do something.