Does a pending case give my son a status after the petition has been approved?

An approved Form I-130 petition gives no status and unless the priority date is current, an approved I-130 cannot be used to file a Form I-485 adjustment of status [green card] or a I-765 work permit. In order to adjust status when his I-130 petition becomes current, he must maintain his status. And under the circumstances, he should consider applying to reinstate his status by returning to school if that is still possible at this point. If he does not his I-485 [green card] application will likely be denied by CIS for failure to maintain status.

The I-130 does not give your son status. He must maintain status in order to apply for adjustment of status once his priority date is current. You son can apply for reinstatement of his student status if it has not lapsed more than 5 months ago.

Unfortunately, an approved I-130 petition does not give your son any kind of legal status in the U.S. He should consider leaving the U.S. If he stopped attending classes less than 180 days before leaving the U.S., he will be able to receive an immigrant visa when his priority date becomes current. If he stays in the U.S. without a legal status for more than 180 days but less than 1 year, he will be ineligible for a visa for 3 years; if his unlawful presence in the U.S. will be over 1 year, he will not be able to get an immigrant (or any other) visa for 10 years. Considering that his priority date will not become current for, at least, 7 years (8 years if you do not become a U.S. citizen), it might be the best for your son to wait for it outside the U.S. If he stays in the U.S. illegally, he will not be able to adjust status on the basis of your I-130 petition when the priority date becomes current.

No, unfortunately it doesn't and your son won't be eligible to adjust status. He may be able to reinstate his F-1.

No, it does not. He is not eligible for any benefits until the priority date becomes current.