Given a vector valued function, draw curve, find the arc length, and find the curvature

Question

I'm doing some practice problems and am stumped:

Given: $r(t) = \cos(t^3)\,i + \sin(t^3)\,j + t^3\,k$.

1. Draw the curve for $t \geq 0$, using any projections or additions that help explain the curve.
2. Find the arc length of the curve from $t = 0$ to $t = 4\pi$.
3. Find the curvature $K$ of the curve as a function of $t$.

My Conceptual Questions:

1. Can you say that the curve is parameterized by this specific vector-valued function?
2. Given a generic curve, how would you go about finding what shape it is? Can anyone recommend a source of similar practice problems or a way to build intuition about what a VVFs curve will look like? My work: - I understand that this curve is a helix - I think a projection from the side and the top will help explain the curve - I know there is a formula for arc length and curvature

Note: I will continue to update as I work on this problem, it may be a few hours though, I have to go to work.

Thanks for your time :)