"Take a deep breath, dear," Xavier replied with a calm and soothing authority born of two decades of dealing with hormonal and emotional teenagers under his care. "There's no need to rush through anything. Take moment to focus and center yourself," he continued. "The loss of a parent is always upsetting and if you need some time to settle yourself when speaking of it, than certainly take that time. I'm not going to rush you."
Whatever her father may have actually told her, and Xavier wasn't fool enough to believe that Mastermind had ever said he was sorry about his actions against the X-Men, didn't really matter to the man. Charles was certain Regan was saying it only in an ill-conceived attempt to make nice with her father's old foes because she didn't believe she'd get the help she wanted otherwise. Now was not nessicarily the time to point out the falsity of such logic, as the girl obviously still hadn't come to terms with her father's death. But in the near future, certainly.
"I had heard of your father's passing, and I wish I could shed some enlightenment on the how of it, but I cannot. I am happy to know that you are alright."
He wasn't going to touch on the topics of diploma or schooling immediately. Regan was obviously scared of being turned away and probably scared to be there at all, so first he was going to work on calming her down. The surest way to do that was to simply be there and offer some friendly company and words.