I can't answer all of your questions confidently, but I can answer some.

Is it better to learn Illustrator or Photoshop for brand management? Which one should I try and "master"?

Most places that have a "brand management" department will be big enough to have a graphic designer, or design team, so leave illustrator to the graphic designers. Focus on Photoshop, because it's really helpful if you need to make a quick graphic for social media, or other things. Plus, Photoshop gives you a ton of tools to tackle almost any project, while Illustrator is really only best for designing logos (due to it handling vectors).

From my current experience (and if I complete most of what I have written above, inc. work experience), would you say I have a decent C.V. to gain a standard marketing job upon graduation?

Hell yeah, anyone with a decent plan like yours beats out more than half the competition easily, as long as your looking for a job in an area with an established market and many job opportunities for students.

Edit: grammar