Re the telepaths and Earth and the Shadow War:
[spoiler] They recruited Blips, runaway telepaths, to help fight the shadows. We just didn’t see most of them in action for whatever reason (to be fair, we only saw the minbari telepaths do anything like once or twice, the rest of the time the telepaths were offscreen doing their thing).
Sheridan being a douche is actually kind of in character for him, see above, re: redirecting military readiness funds because he didn’t want to pay 50 credits a week for rather spacious quarters. Mind you, his positive qualities vastly outweighed those negative traits of his, but they were there. Like pretty much everybody else on B5, Sheridan was a flawed person.
As far as how they treated Lyta, yeah, that was pretty bad, and I think mostly just the result of some sloppy writing. I guess the long-term point they were working at was that Bester (and later Byron) were both right in a way about feeling that the best interests of telepaths did not align with the best interests of the Mundanes as the Mundanes saw things. The way they both went about things was flawed in various ways.
Earth (or at least, the higher echelons of EarthGov after Clark consolidated his power) was aligned with the Shadows during the war. Presumably the idea was for the Earthers to get into things attacking the younger races (and presumably even the Centauri) after Clark had managed to whip up enough xenophobic fervor with his propaganda.
PsiCorps was similarly allied with the Shadows along with the rest of EarthGov, something that ended up leading to Bester and Sheridan team up (talk about strange bedfellows). Bester didn’t like what the Shadows planned to do with “his” telepaths, and took action to stop it. Once the war was concluded, he went back to antagonizing his good friends on B5.
Byron, IIRC, was a PsiCop, one of Bester’s right-hand men, in fact. So during the War, he was either doing the Black Omega thing or he was on the run as a Rogue Telepath. Given his lack of love for the Mundanes and their political interests, he seems unlikely to have taken a side in the Shadow War. Mostly he wanted a homeworld for the telepaths because he wanted a place where they could be alone from the Mundanes, free to use their powers freely amongst themselves without having to constantly use self-restraint and actively block out everybody else’s thoughts.
He wasn’t looking for a reward for helping out, he was looking for compensation for being victimized. But yeah, aside from his legitimate concerns, Byron was an annoying jerk. I assume he got hair that shiny from using Centauri haircare products.[/spoiler]