As others said, you can bring up anything you want to discuss with your therapist. If there is something the therapist doesn't want to discuss like his personal life he will tell you so you don't need to worry about that. At the same time, if he talks about some parts of his personal life publicly then he shouldn't mind or be surprised when clients bring it up in session though he could still refuse to discuss it.

You are not violating any boundary by googling therapists and researching publicly available information on them. Whatever people put out online about themselves, they make a conscious choice to do so. The act of posting whatever we post online, in and of itself, is a permission for everyone to look at it, otherwise we wouldn't post it if we know that the information goes public. So, I don't see how you can violate anyone's boundary by looking at the publicly available information. And it's interesting to me that this question comes up over and over again on this forum..