Without a great deal more information, it is really difficult to give an exact answer.
An entry level status separation is just the characterizations of the separation, like honorable or general. It is not the actual basis for the separation. For example, someone could be separated for PT test failures and get an honorable or general discharge. The status of that discharge doesn't give a clue as to the actual basis for it, though it does rule some things out.
It isn't a discharge for misconduct, because they wouldn't give an ELS separation status for that. So, it must have something to do with either a medical issue or personality issue, as it relates to military service. That is an exceedingly large area of possibilities though, some of which would allow for reenlistment and some of which would not.
Until you know the actual discharge basis that is being used and the reenlistment code that he is given, it's not possible to know right now if he could reenlist. Is it possible that he could reenlist? Certainly. There are discharges that grant an ELS that allow for reenlistment, so that is possible.
As for getting into contact with him, you don't technically have a legal right to speak to him. He's over the age of majority and in the service, so he is legally emancipated. I don't say this to be insensitive, but it's just the reality of the situation. You can certainly contact the base where he is in basic and ask to speak with his command, or at least ask that a message be given to him to contact you, but they don't technically have to work with you as a parent because he is legally an adult.