If I'm writing a Jason centric fic (like 3ish months post UTRH), but its entirely outsider pov and Hal Jordan is one of those povs, what would be the comics you recomend as essential to understanding Hals character? I want to make sure I'm not just writing a fanon interpretation of him!
Oh FAWK YEAH!!! This era specifically is complex, and a lot of them aren’t what I would call essential to understand understanding his character as a WHOLE, but they are very essential to understand him at the time. 
There’s overlap between UTRH and Green Lantern: Rebirth (not the same as rebirth era Green Lantern!! this is the name of a specific limited run) so he could be a GL again or he could still be the Spectre. My gf wrote a fic about Jason and Dick from this era and had Hal show up as Spectre (it’s bc Spectre Hal is my favorite Hal)
Ok so if you intend for him to still be the Spectre: Emerald dawn I&II (6 issues each), Emerald Twilight (Green Lantern (1990) #48-#50), Zero Hour (start with #5 end with #0), Parallax: Emerald Night (it’s a oneshot), at least the last issue of The Final Night (#4), Day of Judgement (#1-5 is the whole thing, but #2-5 have Hal actually there), Legends of the DC Universe (#33-36), issues #1-4 and possibly #5 of The Spectre (2001) (but I really recommend reading all of it bc it’s my favorite comic of all time and a REALLY good glimpse of what Hal’s psyche was like in the early 2000’s), and FINALLY JLA/The Spectre: Soulwar
If he’s still Spectre it would be after all of The Spectre (2001) so if you want, I can try to summarize the parts I think that would be most affecting him being around Jason.
If you want him to be Green Lantern again, add in Green Lantern: Rebirth. It’s not a great comic and it retcons important parts of the comics I just told you to read but it’s how he got his ring back
And a pretty long list. Sorry!!! You just hit a complicated era, and specifically my favorite Hal comics ever. 
There are a couple things that would affect his actions in addition to what’s in these issues.
If he’s still Spectre he’s currently raising his niece, Helen, who’s at most 10. He decided to take her with him bc her parents were killed by a villain targeting him. AND HELEN bc she’s basically the second coming of Jesus (that’s a bit of an exaggeration, but she canonically has two possible fates. Bringing about a golden age of peace on earth, or committing suicide before she’s 30) AND he’s ambiguously genderfluid. The comic was written in like 2003 so they don’t say it explicitly, but Hal does have a female form, and Helen called that version of her Auntie Hal.
If he’s a GL again it’s been for max a month bc of when UTRH is, and he doesn’t really remember that much about being Spectre (including raising Helen!!) so he’s got around 1 to 2 years worth of memories that can’t be more than vague feelings and impressions. He probably has a lot of déjà vu ESPECIALLY SURROUNDING JASON bc when Hal was bringing Oliver’s soul back to life they saw Jason in heaven. I didn’t put it on the list because it’s literally one panel in a green arrow comic.
