i'm too tired to think about everything else you mentioned there, but i'm going to step in and hold a shield up for feferi before somebody else comes in with a sheild covered in spikes and explosive swords aimed right at you.

Yes, Feferi broke up with Eridan, and yes, this may have been a mistake. But to be perfectly fair, he was not exactly helping the situation any. Even despite his morailigence, he was still a largely violent troll with an open hatred towards lower casted trolls. it's not that feferi WASN'T doing her job, it's that she COULDN'T do her job, she simply could not hold back the massive charging train that was Eridan's instability and could only instead slow it down as much as she could. If there was a more pacifying troll such as say Kanaya or Nepeta (Eri/Kan seecret moirail shipper here, hi.) then maybe things could have worked out better, but the problem was that while on Alternia any other viable options were either already taken (Viriska, Equius) or too far away or unknown to do anything about it. (Various other trolls we never saw.)

And on Feferi's side, she had to put up with this genocidal troll who would often times not listen to her, or otherwise SAY he listened to her, simply to turn around later on and reveal that he really didn't, he was an emotional drain for her, if it was anything like i think it is, it might even have been so bad that there were times when she feared leaving her computer in case Eridan tried to do something stupid or horrible again, and if she wasn't there to talk him out of it, he or everyone around him would pay the price for it!

Eridan was the equivalent of a broken plug that always leaks, and the sink he is attached to is Feferi, and the water is her emotions and sanity. Had she not broken her relationship with him, he might have improved yes, but from what she could see, the only thing in her future was an uncomfortable life of catering to this angry fish boy who didn't even like water with little to no success, and sacrificing all her personal freedoms to do it.

And hey don't get me wrong here, i think she should have kept at it too, i even ship Fef/Eri as both hearts and diamonds depending on the situation. But as it is in canon, and as far as feferi could tell, she could not do the job she had been given, and after so long of trying, she didn't even want to anymore, and had to break the relationship in order to liberate herself, hence the "i'm FR-E-E-E-E-E-E-E" bit as she swam up into her first gate.