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It the point is on the line the distance is 0. If the point is not on the line, then it is possible to draw a unique line from the point to the line which is perpendicular to the line. The distance from the point to the line is the distance along this perpendicular to the line.
Yes, a line and a point can be on the same line. A point can be placed on a line. It will then be collinear.
There is no such thing as a line point.
Substitute the coordinates of the point into the equation of the line. If the result is true, then the point is on the line.
A point lies on a line if the coordinates of the point satisfy the equation of the line.