starting with season 4 because this is the most angering season
(read only the bold green if you don't want the ramble)
he never completely lost his intelligence. his issue is mostly that he went back to being how Ed was before Oswald (I don’t think his whole “I know who I am without him” works yet), like Lee said it was psychological. The after ice effect, lasted for about a week, in which he was completely confused and had trouble concentrating.
It depends on the person I write with, but in the 2nd half of s4 (after the incident with Sofia), Ed can go back to working with Oswald (but still keeping his distance as he tries to figure things out). Although I think that the most likely scenario would be that he goes away for a little (not from Gotham, just from people) as he tries to completely figure out who he is (”without him” and without anyone else). He might pop in every now and then to help or to just cause a little mayhem. However, since he still worked with Lee in the Narrows (in s4a) and thus might have made a few enemies, he and Lee get caught and they get stabbed by them. No matter what details are altered in this timeline, between 4x15 and 4x22, Ed continues his mission to get rid of abusive assholes, only this time he actually kills them
He does not try to get hurt and go to arkham later solely because of Lee. Since he feels rather lost in the first half of the season, Ed’s mental health declines severely and it goes to extremes. Part of those episodes, is him being afraid he is going to hurt Lee, of course. He does not want to acknowledged he needs help of course, he self-medicates and it only gets worse. He still pretends everything is okay and he presents the fight club in the narrows and spends his time there.
he and Lee were NEVER romantically involved. He doesn't admire her either. He certainly cares about her and he even considers her his friend, especially during the first half of the season. Part of Ed wants to fall in love with her, because well, she is a woman and she is nice to him, but he can’t and he won’t and he certainly stops wanting that after 4x15. // still, I like the idea that everyone assumes Lee & Ed are together and sometimes they go along with it (but they haven’t kissed once or want to), but in reality they actual friends and they are the best gay/bi icons in the Narrows. Lee also helps Ed accept that “it’s okay to be gay/bi” and his feelings for Oswald. (things I'd love to happen here & here between 0:48-1:06)
S4 could be a time to explore more dynamics too, such as Lucius & Ed. Them solving crimes together? please and thank you! and more!