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2
4 points define a plane.
No, 2 points define a line, 3 points define a plane.
No, two points define a line. It takes three points to define a plane.
It can allow you to define shapes but that is not quite the same thing as an object.
3
2
Three.
Two.
The two foci are necessary to define the location of an ellipse, but the shape depends on the eccentricity, which is related to the lengths of the two axes.
4 points define a plane.
No, 2 points define a line, 3 points define a plane.
No, two points define a line. It takes three points to define a plane.
2 points
To create a plane, infinitely many. But to uniquely define one, 3 are enough.
It can allow you to define shapes but that is not quite the same thing as an object.
In Newtonian three dimensional space, two points can create a line, three to "define" it. In Einsteins "time-space", a minimum of four points are required.