All of these points are not collinear. Consider them as the vertices of a triangle ABC. Recall that the perpendicular bisector of the sides intersect at the circumcenter (which is the equidistant point you're looking for). By finding the intersection of at least two perpendicular bisectors passing through the midpoints between say, A and B and A and C, we find the equidistant point.

I'm not sure I understand 2.