Your son would lose his H4 status once you lose your H1, but if an I-485 is pending for him, he would not be out of status. He doesn't need an EAD to maintain status when he's not working. You need to find an AC21-compliant job ASAP, using your EAD if necessary, so your I-485 doesn't get denied.
ALL people on the tax return need to have SSN to qualify for sitmulus payment. I had similar case. I had a SSN but my wife had ITIN. We did not receive any stimulus payment for the same reason. IRS clearly states that if it is a joint return, both (or all in case of kids) need to have valid SSN