Do you let him talk about his dad during the day? He's obviously desparate to! I know it's horrible but you need to have a talk with him about the situation, in terms that he can understand. And tell the truth, as much as you can, so Daddy is not working away, he's left.
My DS is 4 too and when exP left we (we both sat down and talked to him, about a week after exP initially left, when the affair was discovered) told him that Daddy was not going to live with us any more but that he'd still see lots of him, that we both still loved him very much etc etc. We tried, as much as possible, to present it as things changing, but not necessarily for the worse (you really need to keep your own feelings out of it for that to work!)
DS has woken in the night upset a few times. I did let him ring exP once, at 4am as it was the only way he would go back to sleep. I figured that if I had to be up at 4am listening to our crying child, then so did exP! Other times, I've sat with him while he goes back to sleep, or once I went to get the phone and by the time I came back, he'd gone to sleep...
To be honest, I don't think you can separate out "other issues" from your son sleeping. If he's feeling anxious and stressed about what's happening during the day, it's going to come out during the night.
Sorry you are going through this too, it really does suck.