TLDR:
It seem to be the Fn key and the F4 key (toggle microphone), which seem to break everything.
I still have no idea which program is responsible or how to fix it permanently.
Long version:
I tried xinput disable 13; sleep 1; xinput enable 13.
In addition I disabled and enabled 15 and 16 (and maybe 11).
It didn’t help (at first. More on that later).
I wasn’t able to disable 2 or 3. It failed with the following message:
X Error of failed request: BadAccess (attempt to access private resource denied)
Major opcode of failed request: 131 (XInputExtension)
Minor opcode of failed request: 57 ()
Serial number of failed request: 21
Current serial number in output stream: 22
In the beginning I was not sure how useful it is to watch what keys are considered as “down”. Since it starts with all keys “up”, I think keys staying down is a result of the error, not its cause.
However, since xinput disable 13; sleep 1; xinput enable 13 allows me to reset all keys to “up”, I finally could map the behavior of the keys systematically.
Pressing the Fn key a few hundred times:
- Sometimes it changes the state of key[64], key[77], key[83] and key[151] to “down”.
- Sometimes it changes the state of key[64], key[71], key[77], key[83] and key[151] to “down”.
- Sometimes it changes the state of key[64], key[70], key[71], key[72], key[77], key[83] and key[151] to “down”.
After releasing the Fn key, sometimes either key[64], key[70], key[71], key[72] or key[151], but only one of these keys, stays down.
In addition at one point the key[108] went down and stayed down for the rest of the test.
Furthermore, at some instances when I pressed Fn
- either the terminal changed its appearance (toggle full screen),
- the small window for showing and adapting the brightness of the screen appeared
- a “Close all tabs?” window appeared,
- a “Logout window” appeared or
- the small window for changing the microphone appeared.
Most often it was one of the first two behaviors.
Pressing Alt:
key[64] and key[77] change their state to down, but only until you release the key.
What happened now?
At this point I wanted to continue with ‘4’, ‘5’, ‘r’, ‘t’, ‘f’, ‘g’, ‘c’ and ‘v’, but then I noticed that the keyboard was now working normally, besides the Fn key (and some of the the F1-F12 keys?). Sadly, my mouse/touchpad stopped working and I was no longer able to click.
Since the problem might have started when I was trying to reduce the brightness of the screen, I started to try F1-F12, sometimes in combination with the Fn key.
I was not sure what exactly was the cause, but the problem with the keys ‘4’, ‘5’, ‘r’, ‘t’, ‘f’, ‘g’, ‘c’ and ‘v’ reappeared. On the other hand my touchpad started to work again.
FYI: I was not able to end the watch command with Ctrl+c. I had to use the mouse.
I pressed Fn multiple times (and inbetween restarted device 13).
In addition to the strange behavior already descriped above,
- at some point the LED of the key started to glow, but I was no longer able to click with the mouse
- at some point I was able to click with the mouse again and
- at some later point the keys ‘4’, ‘5’, ‘r’, ‘t’, ‘f’, ‘g’, ‘c’ and ‘v’ started to work normally again.
Systematically checking the F1-F12 keys:
The LED on the Fn key glowed while I was performing the following tests.
Pressing F1:
key[67] is down and a “Do you want to read the Xfce Terminal manual online?” window appears. The letters continue to work.
Pressing F2:
key[68] is down and nothing happens. The letters continue to work.
Pressing F3:
key[69] is down and nothing happens. The letters continue to work.
Pressing F4:
key[70] is down and nothing happens. The letters continue to work.
Pressing F5:
key[71] is down and nothing happens. The letters continue to work.
Pressing F6:
key[72] is down and nothing happens. The letters continue to work.
Pressing F7:
key[73] is down and nothing happens. The letters continue to work.
Pressing F8:
key[74] is down and nothing happens. The letters continue to work.
Pressing F9:
key[75] is down and nothing happens. The letters continue to work.
Pressing F10:
key[76] is down and File menu of the terminal is toggled. The letters continue to work.
Pressing F11:
key[95] is down and full screen is toggled. The letters continue to work.
Pressing F12:
key[96] is down and nothing happens. The letters continue to work.
Pressing Fn+F1:
key[64], key[77], key[83], key[151] + key[67] are down.
The LED of the Fn key stops to glow.
A huge amount of dom0 menues (more than hundred, probably less than two hundred) are opened. I have the following options: Open in New Window, Create Launcher…, Create URL Link…, Create Folger…, Create Document, Paste (grayed out), Open Terminal here, Arrange Desktop Icons, Desktop Settings…, Properties…, Applications
To get rid of the menues I click “Open Terminal here” more than a hundred times and then close the terminals.
The letters continue to work.
No that the Fn key does not glow, I repeat the test of the F1-F12 keys.
Pressing F1:
key[121] is down and the loud speaker is toggled. The letters continue to work.
Pressing F2:
key[122] is down and the volume of the loud speaker is reduced. The letters continue to work.
Pressing F3:
key[123] is down and the volume of the loud speaker is increased. The letters continue to work.
Pressing F4:
No key changes its state! The microphone is toggled. Whenever the microphone is off, the strange behavior reappears.
Pressing F5:
No key changes its state! The small window for the brightness of the screen appears, but the brightness does not change.
Pressing F6:
No key changes its state! The small window for the brightness of the screen appears, but the brightness does not change.
Pressing F7:
No key changes its state! The “[Dom0] Display” window appears. The letters continue to work.
FYI: The symbol of F7 in my keyboard shows a camera, not a display.
Pressing F8:
No key changes its state! Nothing happens. The letters continue to work.
FYI: The symbol of F8 in my keyboard shows a crossed-out Wifi symbol.
Pressing F9:
No key changes its state! Nothing happens. The letters continue to work.
FYI: The symbol of F9 in my keyboard shows a gear. Maybe it is a symbol for “settings”.
Pressing F10:
No key changes its state! Nothing happens. The letters continue to work.
FYI: The symbol of F10 in my keyboard shows a magnifying glass. Most likely it is a symbol for “search”.
Pressing F11:
No key changes its state! Nothing happens. The letters continue to work.
Pressing F12:
No key changes its state! Nothing happens. The letters continue to work.
Conclusion: As long as I press Fn key never again and press the F4 key only an even number of times, I have no problem.
Real conclusion:
There is some problem with the Fn key and at least some of the F1-F12 keys.
I still find the behavior of the Fn key the most worrying. Fn seems to not only toggle between two states but switch between an unknown number of states (touchpad enabled/disabled, Fn yes/no, Fn key glowing yes/no, various different keys down or not).
Thank you, tzwcfq, for bringing me and this analysis this far. 
Any ideas on how to continue from here?