I think Festing could have survived this debacle if he had cooperated with the investigation.  When he refused to do that, and resisted the pope's authority, there really was no way for him to continue. The only thing that surprised me is that the situation came to a head so quickly -- but again, given that there really was no way forward for the Knights with Festing in command, I guess there's no real surprise in the speedy resolution of his situation.
The appointment of a pontifical delegate effectively neutralizes Burke, but it's only a band-aid. At some point, obviously, Burke has to be replaced so that the Knights can resume normal relations with the Holy See. I imagine that's being negotiated already.