A regular polygon will tile it if its internal angle divides 360 degrees.
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Not always
Not by itself.
A polygon (or any other plane shape) is convex if you take any two points inside it (or on its boundary) then the line joining those points is wholly inside (or on the boundary of) the polygon.
No.
No, but a pentagon is a polygon. A polygon is a plane shape with 3 or more straight sides.