after she zaps each hair she pulls it out with a tweezer, is this normal?
Yes.
Without taking the hair out, how does she keep track of the hairs that have been treated, vs. those that have not? Furthermore, would you want to leave the office with a face full of hairs that you have to wait for them to fall out on their own? Most people like the idea of having a bare treatment area when they are done with their session.
You need only worry if you feel the same sensation as you pulling one of your hairs out by the root when your practitioner removes the hair after treatment. Although most will slide out effortlessly, a slight “popping” sensation is not a sign of bad work. When you feel it, you will know the kind of “pop” I am talking about.