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Yes, all geometry planes are infinite and have lines going in every direction, except it doesn't look like that when you see a grid because they only need to include some information for a certain part of a line of the plane. All lines go forever in each direction (left and right), and a grid is made up of lines.
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Can three lines intersect a on point?
Yes, in Euclidean geometry, an infinite number of lines can meet at one point.
How many lines contain n points with no 3 points collinear?
None. In ordinary geometry, a line contains an infinite number of points and, by definition, they are all collinear. In projective geometry, however, you can have three lines in the form of a triangle. Each line has only two points on it, so it cannot have 3 points collinear.
What has infinite length but no width no thickness and no endpoints?
It is the parallel lines in Geometry!
Can three coplanar lines intersect twice?
In Euclidean planar geometry, not unless they're collinear, in which case they intersect an infinite number of times. In other types of geometry ... maybe.
In elliptical geometry do two points not determine a unique line?
No. In spherical elliptical geometry, for example, given the earth's North and South poles, there are an infinite number of lines of longitudes between them.
