Tout is not a noun, it is an indefinite adjective. It therefore needs a noun (or a pronoun) to go with. This is why you can agree it: “tout le monde” (masculin singulier), “tous les enfants” (masculin pluriel), “toute la famille” (féminin singulier), “toutes ses copines” (féminin pluriel). Treat it as a numeral adjective, if you’d like.

You can use it by itself, but in this case it replaces the whole nominal group and means “everything”, “the whole”. Ex: “Tout va bien”.

In this sentence, the subject is “Tout ce qui”, and it is the subject to the verb “brille”. Then, “tout ce qui brille” is the subject to the verb “est” (or in this case, “n’est pas”).

You cannot have two juxtaposed subjects to the same verb, so you would have “tout brille”, meaning “everything shines”, but here you have two distinct “propositions” (segment containing a conjugated verb), so each of them needs a subject.