PY, when I was in YU (for one year), I didn’t learn any kefira. We didn’t learn biblical criticism. There may have been classes that you could sign up for, but I don’t know. They have Judaic studies requirements (in Stern its 3 classes a semester). You get to choose what you take, but you do have to take a certain amount of tanach and some other requirements. The class I took in Vayikra was just a standard class with meforshim, nothing that was a problem according to anyone’s standards (except Satmar). There were gemara classes offered for women, but they were optional. Most women did not take them.
As for art classes, the art classes I am aware of given at Stern were the kosher ones. Anything that was not, was given at Pratt and taken at your own discresion. I don’t think there are any majors that require Art History unless you are majoring in art (in which case, enter at your own risk).