You're asking for more specific rules about how Tongue of the Sun and Moon works, but you've already quoted all of the relevant text. There are no more relevant rules.
This is pretty much entirely in the realm of "Ask your DM". 5th Edition is a lot less precisely specced than 4th, or even 3rd, and this kind of question about what happens in situations where something isn't called out directly in the rules is supposed to be handled by the DM. There are no mechanics for how "touching the ki of other minds" works on a spiritual level, so this is well within the bounds of DM rulings.
That said, in one of my games, I'd allow you to do basically whatever you wanted to do with that ability. I feel that class features should always be benefits, not hindrances, and that creative play should be rewarded. Want to talk to some people, but not others? Great! That sounds like an interesting and non-linear way of using that ability. Want to purposely not understand someone speaking Demonic, since they may be cursing you? That'd work too.
For your third question: I'd run it that you don't have to know that someone is specifically listening, if you don't want to. Like, you could say something to an apparently empty stadium filled with invisible people with the intent that everyone who can hear you can understand you, and everyone would understand you, even if you don't really know that they're there.
For your fourth question: You're not really affecting people with anything, per se. Since there's no mention of a range, or any kind of targeting constraints, I'd run it that you could speak and understand anyone, anywhere. If someone broadcast a message on a TV in a different language, I'd let you understand it.
The specific entry in Tomb of Annihilation in regards to purchasing a copy of Volo's guide says:
Any time they (the characters) want to know lore about a particular monster described in the book, give them useful tidbits from Volo's Guide to Monsters. Do not impart game statistics, since such information would not be available in-world.
Read them the lore. Don't read them the numbers.
Best Answer
No, this won't work for several reasons
There are several problems here...
Qualith is not the written form of Deep Speech. Deep Speech does not have a written form. It is the only language listed in the PHB that lacks a script used to write it down (see PHB/Basic Rules Chapter 4). Qualith is a unique, written-only language only used or understood by Mind Flayers. (MM, p. 221) There is nothing in any book that I can find that links it to Deep Speech.
Secondly, while a Changeling can take an Illithid's form, they do not acquire the mind of an Illithid. As stated in the above linked text:
A Changeling's Change Form states...
(Changelings, WGtE, p. 61)
The languages you speak is a 'game statistic.' Thus, shapeshifting does not grant you new languages. You can't shapeshift to look like a dragonborn and auto-magically learn Draconic.
So, you don't get an Illithid's brain out of the deal, and Qualith is a unique written language only understood by Illithids because its construction is so alien that it makes no sense to anyone else. You could, theoretically, use your face tentacles to touch the tactile bits that make up Qualith, but you won't understand it any more than if you did the same thing with your fingers.