It extends in both directions (up and down) such that it is parallel to the y-axis.
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The slope of a straight line is commonly described as rise over run. In other words, it's the ratio of the change in the y direction to the change in the x direction. Therefore, lines with greater slopes are closer to vertical. A vertical line has infinite slope, and the slope of a horizontal line is zero.
No. "Vertical" just means they go from top to bottom; it doesn't give any information about the length.
No, the horizon is horizontal. A vertical line is perpendicular to the horizon.
Suppose the specified line has gradient m. Also suppose the specified distance is d.Then x = sqrt[d2/(1 + m2)] and y = m*x.A translation, by a distance x in the horizontal direction and y=mx in the vertical direction will move the point by the specified distance in the direction of the specified line.