Hi Wanda. The verb “quiet down” absolutely is separable, but…. In modern English, the only thing that can separate a separable verb from its particle is the direct object: “Mary quieted her children down.” If there’s no direct object, then there’s no way to separate the verb. An intransitive verb, or any verb used intransitively, is therefore not separable. Simple.
In answer to your other question “where are the professional English teachers?” — feel free to inbox me (with just the number of the question, not the whole link) any time you have something particularly interesting.