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Through any three points there is exactly one plane cointaining them?
I think you mean: Are any three points contained in exactly one plane? only if they're not collinear... I think
Through any two points there is exactly?
one plane LINE
If four points are collinear they are also coplanar?
Yes, since any line can be contained in a plane.
Is there exactly one line through two points?
In plane geometry there is exactly one straight line through two points. There can be any number of curved lines.
Three what points determine a plane?
Any three points will determine a plane, provided they are not collinear. If you pick any two points, you can draw a line to connect them. An infinite number of planes can be drawn that include the line. But if you pick a third point that does not lie on the line. There will be exactly one plane that will contain the line and that point you added last. Only oneplane can contain the line, which was determined by the first two points, and the last point.
