This article focuses on the interactions between Mr. Pickels and every other main character he has interacted with.
Mr. Pickels is best friends with Lammy and it is obvious that she is his only friend. He acts hostile towards the other characters she interacts with, mostly with female characters. Despite this he's usually immobile even when he's in close contact with other characters.
He is seen with Cuddles in You're Kraken Me Up, but doesn't try to kill him. However, it's possible that this could be because Lammy was holding him and therefore he was unable to act.
Mr. Pickels appears to dislike Giggles, as he does with everyone else who interacts with Lammy. In Royal Flush, he attempts to kill her by cutting her with a deck of cards before Lammy does it herself by accident.
Mr. Pickels is neutral with Handy. In A Bit of a Pickle, it's hard to tell if Mr. Pickels intentionally meant to kill Handy with his truck or if he just meant to drive and Handy just happened to be in the way.
Despite the fact that Lammy appeared to be friends with Nutty in All Work and No Play, he doesn't try to kill him.
Just like Nutty, Lammy is friends with Sniffles in All Work and No Play and Mr. Pickels doesn't try to kill him.
Just like Giggles and Petunia, Mr. Pickels dislikes Flaky and doesn't like when she interacts with her. He tries to kill Flaky when she witnesses Lammy killing Petunia in A Bit of a Pickle and kills Flaky after allowing himself to get eaten by her in Royal Flush. In The Chokes on You, Mr. Pickels doesn't try to kill Flaky since she keeps to herself.
Obviously Mr. Pickels is very close to Lammy. Though it's unknown why he sometimes gets her into trouble, like when he ripped the head of Petunia's toy bear. Despite the trouble he puts her through, Lammy still enjoys his company and clearly reacted positively when he visited her in prison in A Bit of a Pickle.