When he has successfully completed his counseling would likely be the best time, although if he has substantially finished it, that would probably look all right in the eyes of the court.
The judge is unlikely to question him about the no contact order. Defendants will almost always say that a no contact order was not necessary in the first place. And, it's certainly in their best interest to have it dropped, so naturally, whatever they would say is going to be biased in their own favor. In other words, a defendant is really not the best person to ask about dropping a no contact order. The victim's opinion and feelings are really the most important considerations for the judge.
I can't tell you what to say, because it would be unethical for me to put words in your mouth. You have to explain to the judge in your own words why you want to have the no contact order dropped. If you are honest and sincere about it, the judge will be more inclined to believe you and honor your request than if you were to use someone else's suggestions.
I've never seen a judge, on his/her own, review phone or email records. For one thing, a judge would not have access to these sorts of records unless he/she subpoenas them, and a judge is highly unlikely to do this. If one of the parties obtains such records and presents them to the judge as evidence, he/she will review them, but it very likely won't happen on the court's own initiative.
Hope this helps.