Secret Agent Z-2 is an agent with the American Secret Service.
The activities in which Z-2 is shown dealing with are a good mixture, much as might be thought for the organization. A couple are fighting criminals and a couple are protection details. None are real espionage related per se but with a moniker like 'Secret Agent Z-2', it would not surprise me if there were undocumented escapades that did fit.
Z-2 is a male likely in his late 30s based on the drawings. He is solidly competent and not afraid to mix it up with the bad guys when needed but he is also not particularly rash. For that reason he does not routinely get bobbed on the head as other comic book spy characters were shown to endure during the same time frame. He is good with a gun, as would be expected, but again he does not go in for shoot-first behavior. He is more mature than many of his contemporaries.
We know nothing about Z-2. "Cloaked in anonymity, Z-2 is the country's foremost secret agent. His name never is disclosed, for revealing this might result in harm upon his family and close friends." That is the explanation given to why we are told so little about him. He may have a family (wife and kids) for all we know. In fact, it would not be unreasonable for we do not see him taking any particular interest in any female, including the beautiful daughter of his boss with whom he work.s
Speaking of the daughter, her name is either both Lola and Betty (the first case she is called the former and the second she is called the latter) OR they are twins. Either way, she/they play an important role in the first two missions but are never seen or mentioned again.