I have absolutely no natural ability with math, and doing everything the long way helps me understand the math in an intuitive/visual way that is more easily processed by my mind.
I see, forgive me for assuming you'd want to do it the easiest way possible, it's quite common around here since C2 does such a great job of simplifying things. It's a really good idea to do it all from scratch to get a deeper understanding of things, I often do so myself.
Is there any advantage to using expressions beyond simplified code (such as running faster)?
Not at all, except you might get things done in fewer events, which would help people with the free version to keep their project under 100 events. It's pretty much doing the same thing you do with your own calculations, but even if there were a few more calculations to go through, it wouldn't affect performance in any noticable way.
I can't look at your .capx right now, but for ground rotation I would suggest you use ramones' solution, layer rotation has become much more viable (or at least easier) now that the collision rotates with it. (a few updates ago it didn't)