Right now, the characters in the show have been working with the theory that David is mentally stable and that his delusions are just his powers manifesting, but they’ve had little success in proving that.
Yes, Charles Xavier is the father to Legion’s main mutant David Haller.
Could Patrick Stewart’s Professor X be powerful enough to get David in control of himself?
The comics version of David Haller is not entirely different from the show version, although it’s very clear that David has mental issues on top of great power in the Marvel comic.