The answer is 1.
Here is the theorem:
There is a unique circle passing through points P1 , P2 , P3 if and only if these three points are non-collinear.
The proof is not too hard, but involves some linear algebra. I will post a link to it.
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just one
If you are talking about straight lines, the answer is NONE, because that is what noncollinear means. If curves are allowed, then the answer is infinitely many.
Yes a plane can always be drawn three any three points, whether they are linear or not.
A plane
Three.