Yes.
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No. Equilateral triangles will tessellate and a triangle has 3 sides, which is an odd number.
Only an equilateral triangle, square and a regular hexagon can be used to make regular tessellations but there are innumerable polygonal and non-polygonal shapes which will tessellate by themselves, and others which will tessellate along with other shapes.
No. It is not possible to make a equilateral triangle that is obtuse.
An equilateral triangle has all equal sides. "Equal"ateral
Put one angle of each triangle at the center of the hexagon.