How do the pigeon and octopus kwamis' powers work?
Mimic and Besil were both mentioned in the artbook. Besil was mentioned to be the Kwami of foolishness and the companion fairy (kwami) to Mr. Pigeon. Mr Pigeon is mentioned to be an incredible inventor- but is misguided into believing that pigeons are a superior species. It's easy to assume
Mimic was never assigned a power- but considering that in Ladybug PV and Super Lady Luck the mime was shown to have mime powers (mimicking a bomb, a gun, and a heavy weapon) it's easy to glean as to what powers a fairy such as Mimic would give.
Neither of them have a miraculous. The artbook mentions that Null had trapped Plagg and Tikki in the ring and earrings- so they were the only ones to have them. Implying, also, that at least Mimic was largely okay with the Mime's actions, considering that they are free-roaming.