I can tell you with 100% certainly that he will not "Lose Himself". Kids are often like mirrors and mimic and playback everything they see. Sometimes its because the behavior they saw caused a reaction by someone else and sometimes it is because the behavior looked attractive or cool to the child. This is a very very common action from children and even adults. It is a known fact that if you place a person around someone who acts a certain way.....such as aggressive or loud those around that person will slowly pick up the mannerism of the more noticeable person.
Children typically try to fit in with those around them, if the child is playing with children who act in this manner the other child will start picking up these mannerisms. The old saying "Your friends will influence you" is still very true in todays society as it was when we were kids.
Now for correcting the issues......since you are already punishing him for his bad actions adding a punishment for this may push him so far that he totally acts out since he is always in trouble regardless.
What you want to do is find a way to praise him.........when he does not act out make sure you give him some good attention. Often enough we only pay attention to the bad behavior. When our children act as they should we often take it for granted that it has been a good day and walk it off. Every time he has a good day or a good action make sure you take a moment to get on his level and let him know how proud you are of his behavior. Make a point of bringing up the bad behavior. Such as:
"Thank you son for doing such as good job in the store, last week when you threw that fit it really upset me, and I am so proud of you for controlling that behavior today". Then if you have a little reward like stopping for a ice cream or maybe even a extra cookie at snack time with another "Thank you for that great behavior".
As for the mimicking you need to address it everytime......not with a punishment but with something a little simpler. Immediately get his attention, and let him know that this is not the way we act or talk and until he can talk in his normal way you will not fish the conversation. If it is the laughter, stop laughing immediately. Let him know that you miss the old laugh and when he mimics someone Else's laughter it upsets you and makes you miss his laughter. Then ask him if you can please hear his laugh.
If he continues..........then tell him you do not like it when he acts like this so he should go to his room until he wants to act like himself again. This is not a punshment....do not force him to not watch TV or play with his toys. It is just a way of telling him that you do not care for his mimicking and do not want to see it.
This may take a few weeks.....but be consistent. If you are out in public let him know you do not like it. He may continue but make sure when you get home that you tell him again that you do not like it and want him to go to his room for a while to think about how this upset you.
The reality is he is going to mimic his friends to some extent........so try and keep this in mind. He is still very young and with time he will drop this behavior regardless. In the end this is one of these stages that with time and reminding him he will outgrow.