The only reason Inoda is working as a janitor at REKT is because he forced Kyoko to give him a position in the company so he can "always be with her," but really, he wants to get closer to Asuna. It's not necessarily cause of the career program. It's related...but not the main reason.
I'm pretty sure most of the students at the SAO survivors school are of legal age to work. The legal age to work is 15, full-time or part-time in Japan. But I think you're mistaken here (and feel free to correct me if I'm wrong), but the school didn't ask them to seek full-time jobs, just that they do an internship. But I still somewhat agree with your critique of these internships. I don't believe anyone in Japan is gonna allow high schoolers on their team, especially in a company as big, important, and most likely as high-maintenance as REKT, no matter the position.
I wouldn't say he's moved on. The main cast are still high schoolers first and foremost, so I don't believe Fujino will just disregard this and have them join the workforce from now on. I think this is just a way to have Asuna or Kyoko discover Inoda is sleeping with one of the aforementioned family members. Thus, bridging the gap to have some oyakodon scenes and have Asuna fall further and further into depravity once she sees how much her mother can't live without Inoda's dick. Something something, it's hereditary... yada yada apple doesn't fall too far from the tree.