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No. The diagonal through a rectangle can be computed via the Pythagorean theorem: c2 = a2 + b2 where c is the diagonal length and a and b are the horizontal and vertical lengths of the rectangle.
A straight horizontal line with no slope
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Not necessarily. Imagine yourself inside a cuboid room. Consider the following three lines: (A) The horizontal line joining the far wall and the floor. (B) The horizontal line joining the wall on your left and the ceiling. and (C) The vertical line joining the far wall and the wall on your left. The line C may be considered a transversal to the other two. These are both parallel but they are not coplanar. Their planes are both horizontal but Line A is in a low plane while B is in a high plane.
The slope of a line is the change of the y(vertical) axis over the x(horizontal) axis. It is the rate. In the formula y=ax+b the a is the slope.