Question

For a given line l and a given point of intersection p, there exist an infinite number of lines that pass through p and are perpendicular to l.

Answer 1

In 3(or more)D, yes.

Answer 2

infinite number of lines pass through any one point on a plane, but the line being perpendicular to the other line makes this a specific case. Look at the diagrams and see if they points to the answer.