Taking the Corleone characters fully into consideration through all the movies and books about them:

Fredo was not a "made man" in the sense that he never killed anybody (read The Godfather Returns).

He was a Capo on the same line with Sonny, but I think only because he was Vito's son, nothing more. Everyone knew "Fredo was...well Fredo..." So I think he was only there because he was one of the sons.

He'd have a gun just because it's like giving a child your keys to play with. You never expect your kid to start up the car and drive, but if it makes him happy why not?