I'm gonna answer which of these I can. I will be making reference to a number of out-of-game texts, since the metaphysics and the character of Vivec (as written by MK) is heavily expanded outside the game, 36 Lessons excepted.
Mysticism is related to CHIM generally because CHIM is a part of a mystic (esoteric) system of belief. Mysticism is all about secrets, self-power and various hidden potentials of magic contained within the self and the universe, to describe it very vaguely. And CHIM, or any of the states similar to it, can be seen as the crowning achievement of such a study: complete rule of the self that manifests magically upon the outside reality.
Xarxes I don't know about. While there are plenty of myths about him, I don't think they occur in connection with CHIM or the Tower. Although he has a connection with Thief symbolism, like Vivec, via Arkay the guardian of the Thief constellation.
Aedra may not be aware of CHIM because they may not be aware of anything at all. It depends how literally you take their "death" at the convention. However, they seem to manifest bodily on occasion and interact with us, so it is possible they have a knowledge of it on the level of mortal scholars. It's important to remember that in Dunmer faith, Aedra represent all the laws of the world that should be overcome: CHIM is probably rather at odds with Aedric belief. The Daedra, however, have much more of a connection, based on the http://www.imperial-library.info/content/loveletter-fifth-era-true-purpose-tamriel:
This section is talking about the creation of Oblivion through rebellion, and Liberty, which is basically how CHIM is characterized in the Loveletter. This isn't necessarily talking about CHIM itself, but rather the general push towards transcendence and victory over the Aurbis. Also, CHIM is the title of a section in the http://www.imperial-library.info/content/mythic-dawn-commentaries, connecting Nu-Mantia and CHIM with Mehrunes Dagon.
As for the question about Lorkhan: well, it's interesting to note that Vehk believes Lorkhan didn't achieve CHIM, as stated in http://www.imperial-library.info/content/vehks-teaching:
While Lorkhan's power and revelation certainly paved the way to Vivec (or rather, ALMSIVI as a whole) attaining their god state (possibly the same thing as CHIM), it wasn't as a result of them directly copying him. However, as for whether the Tribunal knew about the immateriality of the universe during the strange events of Red Mountain: well, Vivec claims they were well prepared, in this section compiled from the http://www.imperial-library.info/content/trial-vivec (http://www.imperial-library.info/sites/default/files/forum_archives/Trial3.htm):
And the reference to Magnus certainly suggests arcane knowledge about the nature of the Aurbis, since he's one who escaped it (or part of it).
There is a sort of connection between CHIM and the Psijic Order, but it's not a direct one. Vivec speaks about this, again in the Teachings, where the difference between the Psijic Order and the Endeavour is noted:
See at the end the connection of the Psijic Order to all these other mystic orders, but the Endeavour's difference is enforced. The Psijic Endeavor can be seen as the path towards CHIM or godlike awareness in every part of the Dunmer history, from Veloth onwards to the Tribunal. The Endeavor is described later in the text, along with CHIM.
Don't worry about asking questions. There's plenty of new answers still to be got.