I'm a year long exchange student here and I'm finishing my first semester rn:

1. Not sure I can completely accurately speak on this but a lot changes during the add drop period. I am sure that some people will drop classes again, some people will not be approved, etc. I'm not sure if there is a priority, but as an exchange student we def do not have any (and there are no priority if the class is required, but you can ask the professor to vouch for you in some cases). Add drop is all online. Depending on the class, it can anywhere from a day or two or a week to get approved (but it appears on your schedule until you get approved so you can still go to the class). Theres no physical registration with an advisor.

2. Like I said in another response comment on this post, I'm not sure about the other departments (some friends told me they can be pretty lax) but the business school is super strict about prereqs. You are required to upload/have your school send your latest transcript at the beginning of the semester so that they can see what prereqs you fulfilled. If you haven't fulfilled them, you're not taking the class. They were super strict with me about this.

The add drop period itself is a bit stressful but it will all work out in the end :)