Core courses are specified courses that students must complete in order to be awarded a degree.

You are bound by the year when you started the new major

You should make a request for the intended major/minor online. Check to ensure that such request is approved before registering for the corresponding courses.

A pre-requisite is a course which must be completed before registration for another course is permitted.  A pre-requisite course provides many of the fundamental concepts required for the more advanced course.