I solved it:

It was, as expected, the BIOS. Right hunch egydio!
After I had restored basic functionality, it became clearer during Windows XP and 7 installation attempts. The BIOS didn't support ACPI. I can't elaborate on details because I couldn't check what the previous version was but it happened with a version 1.11 installed.

So the way to success:

I actually don't exactly remember which way of wincrisis worked, but google it.
I prepared a USB drive with a BIOS. Again, not sure which worked. I tried v1.18, 1.11 and 1.02 but in the end some way worked and it displayed 1.11.

Plugged that USB drive in. I even formatted one with FAT16 which was very slow but might have done the trick.
The way I extracted the .fd BIOS firmware files was:
- Download the BIOS zip and extract the exe
- run the exe on any computer, leave it displaying an error because it won't be compatible
- open task manager, select the corresponding process called something "Insyde"
- right click and say "open file location"
- copy all the files to a temporary location or choose the `.fd file directly and copy it on the USB drive.
- I didn*t rename mine. It was called ZWR.fd

I booted into the special mode:
- Turn off
- unplug power
- hold FN + Esc and keep holding
- plug in power
- press Power button once and let go off this while still holding FN + Esc
- hold FN + Esc for another 1-2 sec and let go
- Left LED flashes blue

One of many tries looked successful - with the light flashing for a few minutes (less than 10, I would say), then rebooting and shutting down.
BIOS was still not accessible, no screen.
Other attempts didn't look as promising, but hey - one of them did the trick and jumpstarted that BIOS.

Anyways. At some stage my Windows 10 SSD that I've put in from another PC finally booted up.
What did I do? Let Windows Update install all necessary drivers and such... forced a involuntary reboot all of a sudden and again - no screen after that. Then, with patience the screen just came on after a few minutes. I could enter the BIOS but no changes to bootmodes would get Windows running again. I didn't have an external Windows 10 install Stick ready by then so I couldn't force it into safeboot. I am convinced it wasn't dead but no interest in wasting time at that ü

So I decided to do a fresh install of Windows XP because I had a CD. That only worked after pressing F7 during install. Due to the unsupported AHCI mentioned earlier. But then, all good.
Windows 7 install also flawless but no drivers whatsoever...
At this stage, I was running BIOS v1.11 and everything looked ok.
Then all of a sudden again, strange behaviour but I could boot eventually. Since then - all good so far. Installed Windows 10 fresh and patched that up with everything. I installed the actual v1.18 BIOS exe from Acer's website either still on Windows 7 or already 10 - don't remember that detail.
The Insyde BIOS update through Windows Update showed up for a while although I had already v1.18 running. So without touching that, after several reboots it just disappeared.



Long story short:
I tried many different combinations with the FN+Esc Bootmode and didn't give up until I had a BIOS settings menu.
I guess the BIOS update through Windows update is the safer way as Acer seems to have trouble with that. That's the first time I saw Windows providing a BIOS update and no one would do that step without some reasons behind. I also never had a failed BIOS install before, now I know - Acer can...
I still don't exclude a hardware error on the mainboard. Because the internal WiFi is and was pretty weak before. For more than a year at least. But at the same time, it'sactually more probable to be an incompatibility of drivers and Windows updates.

Now we wait and see if it stays stable. The original SSD with it's WIndows 10 is back in, adapted all the internal devices again, updated alright and runs smooth.