Since nyrlothotep is a part of nyx and phalimon is the opposite of nyrlothotep Is phalimon also a part of nyx and how was the velvet room created along with igor and his assistants
Well, first thing you need to understand here is that the concepts of Philemon and Nyarlathotep and the concept of Nyx originated in the pens of two different writers. Satomi Tadashi definitely had different things in mind for his lore than Katsura Hashino did when he did his own take on it for Persona 3.
That said, under Hashino’s take, Nyx is the whole reason the collective unconscious exists, so, yes in this canon, Philemon and Nyarlathotep, as part of the unconscious mind which holds Nyx, are aspects of “her” as well in a way; the aspect that wishes humanity’s self-ruin and the aspect which wishes for it to prosper and ascend.
As for the Velvet Room and Igor, they’re Philemon’s creations. The Velvet Room was made as a place to grant Persona Users refuge and aid, while Igor was an experiment of Philemon’s, a doll crafted to emulate a human, in order to study the true meaning of humanity, something Philemon was deeply fascinated with. The other denizens of the Velvet Room (whose origin hasn’t been explained, but I have a whole video with a theory on that on my YouTube channel) display that same desire to find the meaning of their own lives. which is what eventually leads Elizabeth and Margaret to both deviate from the rules they have lived under all their lives.