Three or more sides, no round sides, and it has to be a closed shape.
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It can be but need not be.
It can but need not.
If every side of the polygon is the same length, then it is a regular polygon. If the measure of every internal angle of a polygon is the same as every other, then it is a regular polygon. The two always go together, so you need to check only one of the above criteria.
at least 3 sides
There is no particular name. It need not be a regular polygon - for example, consider a stretched hexagon.