Projective Geometry True/False Questions

Question

These questions are with respect to the projective plane:

1. An ordinary point cannot lie on the ideal line;
2. An ideal point cannot lie on an ordinary line;
3. Every ordinary line cuts the ideal line;
4. Two non-parallel ordinary lines cannot intersect in an ideal point;
5. There are infinitely many ideal points;
6. There are infinitely many ideal lines;
7. There is exactly one ideal point on every projective line;
8. There is exactly one ideal line through every projective point.

Are any of my answers to these questions incorrect, and if so could you please briefly explain why that's the case? Here are my answers:

1. True, because the ideal line is comprised of and only of ideal points.
2. False, because ordinary lines cut the ideal line, and thus go through an ideal point.
3. True, because all projective lines cut.
4. True, because all projective lines cut at precisely one projective point (since they intersect at an ordinary point).
5. True, this is pretty obvious.
6. False, because there's one ideal line.
7. False, because the ideal line is comprised of infinitely many ideal points.
8. False, because the ideal line does not go through ordinary points.