Yes
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Yes. For example a chess board.
regular hexagon, square, equilateral triangle...apex
Yes.
No. Hexagons and squares will each tessellate by themselves but one can not make a tessellation out of hexagons and squares combined. However, if you add in a third shape, the triangle, one can make a tessellation.
A regular triangle, quadrilateral (i.e., square) and hexagon may be used.