Can the distance between two points be zero yet the displacement from one point to the other be nonzero?

Answer 1

No it cannot. The displacement can be zero and the distance nonzero, though. This, due to the fact that displacement takes in account the direction and magnitude, whereas the distance just takes in account the magnitude.

For instance, if we were at a classroom, and I went to the bathroom and come back shortly after to the place were I started, my displacement would be 0, even though I traveled a certain distance.

A simpler example would be the following: You take roll a ball back and forth, say to the exact position where it started. Through the time the ball rolls back and forth the distance it traveled will be increasing, whereas the direction will be canceling itself every time you go back into the starting point (the origin). Thus, distance does increase, whereas the displacement increases at point 2, and decreases in its way to point 1.

Answer 2

Yes, the distance between two points can be zero if they are the same point. However, the displacement from one point to the other will always be zero if the distance between them is zero, as displacement is the shortest distance between two points in a specific direction.