Windows 7 instalation stuck at "Starting Windows 7"

Clicking it leads to regular bios setu, which I have shown before

Insert your win7 install media reboot and select F11 or F12 Boot Menu key as its booting. Is the device shown as UEFI when BIOS is set to UEFI? If not then the flash media is not created correctly.

If either F key isn't working at boot after several tries then try Startup Settings choice in picture I posted above or from the Recovery Menu you posted.

There is no boot list in my bios. Only place where USB is shown and I can manually pick it to boot, is the Recovery for Windows 8, (Use external device to recovery option) and there it is indeed shown as EFI USB Device

There will always be a BIOS Boot Priority order list in BIOS setup. Look on the Boot tab. It is listed there at the bottom. The stick should show up as EFI device there when plugged in. Try External device.

There is normally also a BIOS Boot Menu which is likely what the Recovery is accessing via F11. You said the stick shows up and can be chosen there as a EFI device, correct? Go ahead and choose it to try again. If it fails try formatting it again.

BIOS boot priority menu is not anyhow interactive on my laptop, it is just "Internal Harddrive", Internal Optical Drive, External Device and Network. Nothing else, just that. I have been formatting this stick many times, on many ways, and it has always been stucking on Starting Windows screen with colorful dots floating. Neither of F-keys during boot work, only way to access BIOS and recovery and such is dedicated ASSIST button, which directs to this black menu full of options (not really) that I have shown on page 3 of this post. Choosing this EFI stick boot option in recovery just boots the stick and it is stucking on f-ing windows is starting screen so I don't know what to do. Is there any way to unlock more bios settings maybe?

These BIOS settings are often locked down by Windows 8 which only provides access via the Advanced Options shown in post #25. For this reason I'd reinstall a Dual Boot Installation - Windows 8 and Windows 7
in Legacy mode while deleting all partitions to free up access to the BIOS per normal.

Until then with the Win8 existing you may not be able to install Win7. However when facing the exact same stall you have during 7 Dual Boot with existing factory Win8 keeping all partitions intact, I have resolved it by finding the BIOS setting responsible. That setting may not be present without a BIOS update.