Elizabeth might have fired Hans on the spot, I agree. But she would have done so in a far more reasonable tone of voice. The way that Elizabeth ranted at Paige was entirely personal. Sure, she's angry at Paige for screwing up but even that incredible screw-up doesn't account for the incandescent rage Elizabeth expressed. I suspect that Elizabeth knows that Paige isn't suitable for field work, and she also knows that she herself has very little time left to teach Paige anything and that's all adding to the stress she's already under.

As for Henry, it's really not uncommon for scholarships to only be good for a student's first year at school. The expectation is that the student would reapply for the first scholarship and maybe others. The school would be vested in trying to keep Henry there, but they'd expect the parents to make up for any shortfall if the scholarship ran out. As for the bursar cutting Philip some slack... nope. Philip is incredibly lucky that the guy gave him any grace period to pay at all. when all is said and done, private schools are just a business like any other business. You don't pay you get cut off.