True.
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It's true that a point has no dimensions. But a line has one dimension, not two. A plane has two dimensions, a solid has three, and that's about all that ordinary people can visualize.
Point, zero; line, one: length but no width
Yes.
A line is a series of points extending infinitely in opposite directions. Because a single point has no dimension we get only one dimension when we line the points up.
Anything that has two dimensions and is completely closed is a shape (as opposed to a line which as one dimension, or a point which has zero). A property of these shapes will be that they all have length and height with which area can be calculated.