only if it is regular
if not, no
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A hexagon need not have any equal angles.It can have 2, 3, 4, 5 or 6 equal angles, or 2 or 3 pairs of equal angles, or 2 triplets of equal angles or 1 pair and 1 quartet.
It is a hexagon all of whose sides are of equal measure. Note that it need not be a regular hexagon since the angles need not be equal (in the same way that a rhombus has four equal sides but its angles are not all the same).
A shape with six sides is a hexagon. A hexagon with all sides and angles equal is a regular hexagon.
Yes, they would have to be to make the angles equal, making it a regular hexagon.
They can be but they don't have to be. If they are, then it's called a "regular" hexagon.