Yep that's the way I would've done it, although the trig sub is kind of unnecessary since you can change I to 1/u^2(1-2/u^2)^1/2 then it's essentially reverse chain-ruleable into a standard arcsine/arccos integral
yep, a lot of students don't try in junior years or just haven't learnt how to study effectively so your results then definitely don't reflect your capacity to do a subject.
I agree, especially in yr 10 when teachers don't really know what a student's full capabilities are. I went to a top selective school, and basically none of the students who were at the top of major subjects (e.g. maths, science) remained at the top in yr 11 and 12. Many of the students who...
coroneos is mostly pretty basic though, although HSC hasn't really asked any integrals that have been too tricky in the past few years, it's good to be prepared.