Congratulations! I am also an Animal Science GT so hopefully I’ll be able to answer your questions :@)
I’m currently at a school on the quarter system as well, and for yearlong classes like Biology, CALS will expect you to take three quarters of said class (unless you have AP credit). Most core classes on the quarter system are going to be 5 credits, which will translate into 3 semester credits, so if you have an AP score or 4 or 5 for English, you’ll only have to take one more class to fulfill the requirements. It’s all a bit confusing, so feel free to ask if you’d like me to elaborate.
It sounds like your 2A class is a quarter-long class and will be followed by what I’m guessing is the 2B and 2C course. When choosing classes, make sure to read over the course description because not all science classes are created equal. Some will be geared towards non-majors, some won’t have a lab component, and so on, so definitely ensure your classes will meet CALS standards.
I’m sure they do! UC Davis is actually a really good springboard for AnSci people because they also have a robust program. Chem I and II will be broken up into a three quarter sequence, so as a PreVet student you will probably have to take all of them (unless you have AP credit—as you can see, these exams really come in handy haha). CALS can be weirdly picky about what classes work for FWS (Cornell’s equivalent freshman English class), so I’d definitely send them a course evaluation form for your English classes.
And I’m sorry to hear about that! If you really feel like you can no longer continue as an Animal Science major, I would contact CALS sooner than later and let them know of your desire (and valid reasons) to switch majors. You can actually make the change before you arrive on campus—I did a couple weeks into my freshman year—and your GT requirements will switch over to your new major’s so that you’re not behind when you get to Cornell.
I know this is a lot of information to absorb, but hopefully this helped 
Best of luck!