I did the following without success:
1. RAM can not be removed as it is soldered
2. FAT32 USB Stick with "UX410UAK.bin" on it and pressing Ctrl+HOME on power on
3. FAT32 USB Stick with "AMIBOOT.rom" on it and pressing Ctrl+HOME on power on
(I renamed the 312 version of store BIOS to that)
4. Holding F4 on power on
5. only other graphics output is HDMI. I tried that. Monitor says "no signal" at powering on time and after
6. When you have a look at the pic... I marked the BIOS chip but can not find another Chip in this format. Does it realy looks similar or can this be a different package as well ? If It is a Microcontroller then it definitely looks different. But in that case I can not do a dump. Or it is on the other side?

1+2 I did with your latest version flashed (FX2NV)

=> Last chance is to try out other BIOS versions ? What do you think?

It could be a different package, but normally it would be same as BIOS package. Could be on other side, could be under black fiber protection part at memory slot area, could be under WIFI card
It may be in WSON package, but if not that then I assume it's not used as a separate chip but only contained within the BIOS itself.

Did you make sure all connectors are reconnected as they originally were? Remove any/all USB and tried that way yet?
I see in google this green LED blinking twice for Asus can be something connected that's bad or shorted, you forgot to reconnect something, or bad PSU
What "Green" light it is specifically?

Tried with and without main battery? With and without PSU, so only main battery?

Hold power button in for 20 seconds, what is outcome? Remove HDD, what is outcome on boot attempt

Remove anything external you have connected, like monitor/HDMI Cables etc

Press enter key while green LED is flashing? Maybe it's in standby

No, other BIOS versions wont matter, all would = same/same, what I sent you should be booting, provided write was correct and nothing else is wrong with the board.