1. Yes a circle is a two-dimensional figure. It lies in the plane, which is basically a flat piece of paper that doesn't bend or curve, and the paper extends infinitely in all directions.
2. A circle is <u>not</u> a polygon. A polygon has finitely many straight line segments that glue together to form an enclosed figure. Think of fencing in an area with straight fence portions.
3. Yes this is what makes a circle. Every point on the circle is the same distance from the center. We say these points on the circle are equidistant from the center.