yes. For example the corners of a square, or on the circumference of a circle.
Yes. In fact, given any three non-collinear points, there is one (and only one) circle that passes through all three points.
A plane. A circle can also pass through three non-co-linear points.
You have to have three or more points to have non-colinear points because any two points determine a line. Noncolinear are NOT on the same line.
Two distinct (different) points are needed to determine a line.