It depends what kind of curve you're talking about. if it's a circle, and the line is tangent to the circle, then one. If it's a circle, and the line is not tangent to the circle, then two. But if it's a goofy shaped curve then it could be any number. But the most likely answer to your question is 2.
There are one or infinitely many points.
They are 4 points on the circle, and 29 on or in the circle.
3
There are an infinite number of points on the circumference of a circle and an infinite number of points on a semi-circle so the answer to your question is "An infinite number of pairs of points."
First, just to perfect your knowledge, any line passing though two DISTINCT point on the circumference of a circle is called a SECANT LINE. So we are discussing the special secant line that passes through the centre. It doesn't really have other names. What's special about it though, is the segment of this line that is contained between two points. This line segment is what you are talking about, and the line itself is nothing big. But, the LENGTH of this line segment is defined as the DIAMETER of this circle. Your teacher/friends might tell you that this LINE SEGMENT is the diameter, that is FALSE. Because there are infinitely many such lines can be drawn on a circle. But a circle have only ONE value for diameter. Corollary: Only the set of all such line segments have the length of the diameter of the circle, that's why these lines are special.
none
Lots of points don't lie on the circle. In fact, there are (in a way) more points NOT on the circle, than points on the circle.
50 points
An infinite amount because a circle is a collection of infinite points.
50
5