yes it is
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It can have two congruent sides but does not have to.
In general it cannot be done. In the rare case that the hexagon is regular, select three alternate vertices and draw lines to the centre (centroid) of the hexagon. These will form three congruent rhombi.
A regular hexagon.
Yes - divide the hexagon by drawing a line connecting two opposite sides, dividing it in half. (Drawing a line connecting two angles will only result in two congruent quadrilaterals).
No. They are proportional, meaning that if side A of one hexagon is, for example, twice the corresponding side A' of the other hexagon, then side B will also be twice the size of side B', etc.