Hello, I am really, really sorry you are having a difficult time with Linux. It is, as you say, not a very good start.
The rest of this is off topic, likely not helpful, but might be interesting background.
OK, my guess was fairly correct - your issue is reverse to mine.
I could activate headset but not internal speakers. "Tinkering" with the ALSA slider controls turn speaker on but with white noise - background hiss. Mistakenly switching to head set resulted in an ear splitting scream. Problem was MIC settings.
Eventually found the combination to be able to use both comfortably.
I just have one question, which may seem stupid, but; when you talk about SPEAKERS, are you referring to external or internal?
My issue was internal.
I ask as I had something similar with a friends desk top machine, years ago. She was trying to run desktop (ext) speaker from the same rear output jack as her mic via a splitter plug.
I am not a sound engineer, but I learnt from working on theatre sets that often talent's mic has to be re calibrated several times depending on each "act" as the "gain" often caused squeal. ( a lot of other elect / radio hardware on set) Or the mic wasn't shielded properly. In almost all speaker screeching, the issue is almost always MIC or some other electrical or radio appliance creating "feedback." As I said, this was not a one time fix for all - different stage positions needed different fixes. It's probably automated by now!
My ALSA settings showed a MIC slider, equal to the old GAIN control I worked with decades back so I took a punt and killed that. Problem solved.
Anyway, I just needed to confirm as I was thinking you were referring to built in speakers - you mentioned a tiny Asus.
If they are external, maybe ALSAMIXER is not relevant.
Your post reads you are running Z16 pure?
Or dual boot with another O/S?
Did you use auto install or "something else?"
Did you try a reinstall when the issue first presented?
I ask as I'm just a bit confused by your last para ref the various versions.
Finally, it reads as if you were able to activate the sliders on the first 4 switches, (as shown in your last screen shot) using the arrow keys. Can you include a screen shot please?
Probably not directly helpful, but one never knows - might just be someone else reading who recognises it~
Sorry this is long and rambling, but the more info we can put out, the better the chances of finding a solution.
A writer huh, small world!
Cheers
p