I think the point of the TV show was to present Jazz as what they hoped in their insanity and wickedness to be a model for transitioning especially kids. He does not have a penis, as you say, but a vaginal opening that is actually a wound that has to be kept open with regular (daily I think) dilation with a dildo or the wound will seal up as wounds do. I think it connects to his anus, hence the smell.

Jazz could get the surgery because he was used as a role model for the trans process and the TV show was the platform that enabled it. It probably also got him into Harvard which I think he was unable to hack.

It now appears that unlike so many trans MTF who are gay and thus think they're female, jazz mother screwed him up. It now appears he is actually a mutilated straight man as he now realizes he is attracted to women. As he becomes a more independent adult his real nature is starting to assert itself, but he is ruined as you see. Only religion might comfort him at this point. Hopefully he can live and become a powerful voice against transgenderism.