But to answer your questions, the chapters operate independently so the opinion of one won't affect the opinion of another.
While fraternity rush is definitely different than sorority where it comes to "maximizing your options," since you are going to a new school, I would maximize your options
You probably don't know much or anything about the fraternities at the new school. The rush experience itself can be helpful for you to get to know some guys so you might as well check out several. This would seem like an especially bad time to put said eggs in only 1 basket.