All characters' Tweets are written by Jeph. The characters won't follow any "unofficial" (aka not written by Jeph) Twitter accounts.
QC tweets occur independently of any particular comic or story arc, unless the characters state otherwise.
Characters will not respond to @ replies by non-QC characters, so as not to break the fourth wall. Feel free to Follow them, though, since that is the whole point.
Virtually everything Pintsize posts or links to is horribly NSFW. Click at your own risk.