"And, of course, as we all know, with a computer you can take a simple problem like solve 5x2+2x+1=7 but you can make it harder, for example solve 5x4+2x+1=7. The principle of the problem is still the same."
This is not, in fact, true for polynomial equations of order greater than four. From Wikipedia, "the Abel–Ruffini theorem states that there is no general algebraic solution... to polynomial equations of degree five or higher." This is often featured as one of the main results in an undergraduate abstract algebra course.
I'm all for automating calculations, but the algorithms behind calculations and their proofs are important and often fascinating. Handing students an implementation of such algorithms, e.g. Mathematica, takes away their opportunity to code up the algorithms and understand them deeply.
1. Yes. Bouldering is one type of rock climbing.
2. Very occasionally. It does limit flexibility somewhat, but I wouldn't skip climbing because I forgot my shorts.
3. Both.
4. They're great. Just make sure to get outside eventually!
(edit: formatting)