Mails (and those in the ‘Communications’ tab), contacts (and notifications), bookmarks, and mailing lists you’re in are stored on EVE’s servers and aren’t deleted by transferring. Chat channels you’re currently in are stored by the client so the buyer won’t automatically be in those, but I’m not completely sure about the Player Channels (history of player created channels you’ve joined) section in the (list of chat) ‘Channels’ window as it persists with fresh client settings so I would guess that’s server side too. Chat channels (and I guess mailing lists too) you created will still be owned by the creating character, and transferred characters aren’t removed from the list of channel operators.
API keys are account based, so once a character is transferred from that account the character won’t be viewable with that API key. I think they fixed the ESI tokens persisting after a character transfer too.