I have to ask how I can find the log..
We prefer to get a copy on our log server, which saves storage space here. If you have SSH access, you can activate log level 1 by creating an advancedsettings.xml. Then reboot, run pastekodi from SSH, and post the resulting URL.
Will I have any chance installing an older version?
Let us see the log from latest LE 12 Generic-legacy first.
Is it safe to use built-in kodi commands (Powerdown) to shutdown the device?
Yes. The most important part is unmounting devices, which shutdown / poweroff commands do.
This is precisely what I am currently using, RPI 4B, i thought I could take advantage of these boxes which cost half price !
In that case, Nvidia Shield would be the right upgrade, but it's more expansive.
Make a backup, and try to update. We don't have a GPU whitelist.
Pretty new hardware, so try the latest LE 13 nightly build.
Just put the release build (img.gz file) into /storage/.update, and reboot.
You can use wget to download the file from SSH.
If you're a nerd, make a backup first.
Piracy logic - not our turf. 
I bet you have at least one banned add-on installed. So nice to see such warnings. 
Uninstall all banned add-ons and repos.
Any recommendations what I could try next?
Can you read the FAT partition on your desktop PC? If yes, then maybe your RPi card reader is broken.
LE has many default settings for different remotes included. Some of them are outdated for some buttons.
Use explicit key mapping for volume by creating a remote.xml.
Most add-on developers are at Kodi forum, so ask over there.
Possible workaround: Sometimes you can find streaming links when analyzing HTML radio players:
You can use such links on Kodi (create a playlist). Finding streams on HTML takes time, so that's your job, not mine. 
You use a banned repo, which stops support from our side.
Remove all banned add-ons and repos. If the problem remains afterwards, open a new thread with a clean log.
QBJack Do you have I2C activated at config.txt?
mglae Thanks. The soundcard is not present in the audio device list, so it's still a driver issue.
ps : Is it a kernel problem that doesn't manage HDMI and analogue on the motherboard?
I think the driver is missing at the kernel:
Dec 03 17:49:09.953126 LibreELEC kernel: ALSA device list:
Dec 03 17:49:09.953148 LibreELEC kernel: No soundcards found.Our devs usually add available Linux drivers, it just takes time.