An infinite number in a Euclidean plane - which is the "normmal" plane.
Some selected numbers in the finite or affine planes (but you need to be studying projective geometry to come across these).
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They are parallel lines
A plane is a flat surface
Nobody invented it. It is a simple geometric shape, whose only characteristics are that it is a plane shape and that it is bounded by nine straight lines.
Parallel lines could fit the given criterior
No, plane geometric figures are ones like triangles and circles that can fit completely in the plane. A cylinder needs 3, not 3 dimensions and will not fit in the plane.