No.

But there are straight edge "groups" that are a lot like gangs.

But no, straight edge itself is not a gang, and a straight edge person is not a gang member.

A straight edge is used for making perfectly straight lines when drawing. The straight edge is placed on the paper and you use the edge to draw against.

A ruler has markings, a straight edge does not. In "straight edge and compass" constructions, you are not allowed to mark the straight edge. Things that are impossible using only a straight edge and compass are possible if markings are allowed (for example, it's possible to trisect an angle using a marked straight edge).

Yes, some people in the straight edge scene call vitamin water "straight edge water"

A straight edge is anything with an even, straight edge like a ruler.