Bruce is a Redemption Paladin (though resorts to violence more than a 'typical' redemption paladin because of his own training/being hardened by Gotham). He took on the others for training, but not all took an oath/became a paladin.

Dick and Cass took the Oath of Redemption, same as Bruce. Jason was training to take the oath, but after dying became a Vengeance Paladin instead (and took on the All-Blade). This ties into their main disagreement after Jason returns.

Not all of the bats/vigilantes are paladins. Steph and Kate in particular I don't really see as paladins (Damian is really iffy for me). Barbara I can maybe see as a 'Oath of the Watchers' paladin, but that's honestly more Tim's style (due to his canon monitoring of cults). I want to say Duke is a typical 'Oath of Devotion' paladin, except instead of devotion to a god his devotion is to the tenants of the oath itself (if that makes sense).

Main stories I would do (if I could :p) is a rewriting of UtRH and a longer work around Gotham being cursed (I'm always partial to it being built on a cursed swamp) and the group having to deal with that. Undecided if they'd be able to end the curse or just the constant battle to weaken it/stop it from completely taking over the city.

One: a number of books and authors he reads/references fall under Romantic literature (some satire/critical of the movement, but are still considered as part of it) - Alexandre Dumas, Herman Melville, and Jane Austen are the ones I remember are in the comics. Other notable Romantic authors are the Brontë sisters, Mary Shelley, and Nikolai Gogol.

Two: defining traits of the Romantic movement were emphasis on individuality, emotion, isolation, and celebrating stories about 'common people'. Which sounds right up Jason's alley let's be honest.