Once booted into the live environment, before you install again, partition the disk manually with GParted and then point the installer to your created partitions.
You need to create the following partitions;
1 MB unformatted (this is a legacy from MBR days has to be there for EFI boot)
300 MB formatted FAT32 (this will be your EFI bootloader partition, set ESP and boot flags to ‘on’ for this in GParted, this is also where you tell Kali to install your Grub bootloader too)
Now, you could either split up your drive further and create separate /home etc partitions, or you could just use the rest of the available space as a single partition for Kali, format it EXT4 and tell Kali to install itself there.
In your image it says fastboot is off, that is not the same as secure boot off, are you sure it is off?
Are you sure you told Kali to install Grub to your boot (esp) partition?
If you are only trying to install Kali and have no other OS installed thrn try…
booting into live Kali in GParted delete ALL partitions you can see on the hard disk you want to install Kali on. Create a single partition formatted EXT4 on the disk.
Shut down the system, it shjouldn’t find anything to boot of course at this point. reboot with Kali live again, and point the installer at your only partition now on the disk, then the installer should create the correct disk layout.
The only other thing that springs to mind, if ‘Kali boot entry’ keeps disappearing, check your BIOS isn’t overwriting it because it can’t find Windows, could be a BIOS exploit block type of set up, does sound like this may be happening, if its there, then disappears…
You might have to read up on your motherboard to find out if this can be switched off…
Even after forcing grub install, system information disappeared from UEFI.
I don’t see any info about windows or other os in uefi configuration on my computer.
Another thing, could incorrect system time or uefi version can lead to this?
You have actually checked for a BIOS update for your system, and installed one if available?
It does sound like you have a dual BIOS board, that keeps overwriting your choices back to a default that Windows is expecting.
I would contact the motherboard maker and ask if they support installing Linux.