Why is the support force on an object often called the $\mathrm{normal}$ force?

In the context of vertical forces, in which direction does the normal force $F_n$ act relative to a surface?

A roller coaster car of mass $m$ passes over a hill at point $d$ with speed $v$. The radius of curvature of the hill at point $d$ is $r$. What is the normal force exerted on the rider when passing point $d$?

Three identical boxes A, B, and C rest on horizontal surfaces. Box A is on a flat table, box B is on the same table with an additional weight placed on top, and box C is on the same table with someone pulling upward on it with a rope (but not lifting it off the table). Rank the boxes in order of the magnitude of the normal force acting on them, from greatest to least.

A 3-kg bucket is being pulled upwards by a cord. The tension in the cord is 35 N. What is the acceleration of the bucket? (The mass of the cord is negligible, which means you can assume m_cord = 0.)

You walk into an elevator, step onto a scale, and push the 'up' button. You recall that your normal weight is $625$ N. Draw a free-body diagram. If you hold a $3.85$-kg package by a light vertical string, what will be the tension in this string when the elevator accelerates as in part (a)? Note: Part (a) asked what does the scale read when the elevator has an upward acceleration of magnitude $2.50$ m/s².