Infinite just think about the centre of a circle and its diameter
Infinitely many.
Only one line can be drawn through eight points.
the answer is one
uncountable lines can be drawn through one point.
Infinite lines as for example the diameter of a circle
One.
1 straight line. An infinite number of curved lines.
If you're talking about straight lines (not curves) the answer is one.
Infinite lines can be drawn from a point
Infinite lines because a circle has infinite lines of symmetry.
In Geometry
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.