No it cannot.
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No, the two planes intersect at a line, which is an infinite number of points.
Assuming that the none of the lines are parallel, they can intersect (pairwise) at three points. Otherwise, the question is tautological.
It is the circumcentre, the unique point from which you can draw a circle (the circumscribed circle) which passes through all three vertices.
It is the circumcentre, the unique point from which you can draw a circle (the circumscribed circle) which passes through all three vertices.
polygon