PHEAA has no say over what the consolidation company does. If the consolidation company can provide you with the money to satisfy your debt with PHEAA then you should be able to close that loan.
The PHEAA could be correct that they will not consolidate that debt but if it was already approved I doubt that will happen. These are really questions you need to talk with your debt consolidation counselor about.
PHEAA will need to go to court to get the garnishment. You have a right to be there. They can not do anything this fast.
PHEAA would love to get the garnishment. To do that they have to prove that you are not attempting to make good on your debt. The best thing you can do is keep trying and get in writing from them any of their requests or threats.