As far as the bris, it’s true. By my son, some ladies brought a Rebbe picture and said it’s a minhag to put it under the pillow pillow. So we did. I’m sure there’s a source for it. In general, in lubavitch, a picture of any tzadik is treated like sheimos and wouldn’t be disposed of directly in the garbage.
@DY regarding Nassi hador, the term was first applied to the Frierdiker Rebbe by the Rogatchaver Gaon. When bochurim came to summon him, he said “Der Nossi ruft” by means of explanation to his wife why he wasn’t even eating breakfast first before going.
As far as how were they able to argue with him? Any tzaddik has this role. Hashem decides the rules not us. The role of Nossi hador doesn’t negate other tzaddikim.