Fox was not forced to settle. They settled because they know a drawn out court case would hurt them far more then the payment would. They were screwed and they knew it.
As for Tucker. I think he was fired as a show of strength by Murdock who wants to keep the rest of Fox in line. He had to fire someone high profile to remind everyone he's in control.
We know Tucker was fully vaccinated because we are aware of Fox's vaccine policy. Never forget that.