I had to reinstall Arch due accidentally moving the /root directly, so I did it and then I tried to replace the vanilla /home with my backup /home (backup is 1 day old) and I rebooted with Arch being vanishe, in other words, not showing up in BIOS. Did I make any mistake in the tty ? (Check pic below)
https://www.imgurupload.com/uploads/...3e050aa97.jpeg

I am not sure what the image is supposed to show. I can see a Bash prompt and a few filesystem-related commands, so whoever took the photo must have booted Linux. What exactly is your problem?

Arch should not show up in the BIOS, by the way. If you mean the bootloader menu, you need to fix your Grub configuration rather than mounting filesystems and copying files around.

are you trolling me?
i installed Arch from scratch (succesfully), then i wanted to cp my /home directory from backup device into my Arch then i rebooted and to my surprise there was no Arch in BIOS.

let see if I got this right, you use the bios boot to boot arch(assuming you press some f-key), you booted arch mounted a couple of partitions copied files from one partition to another partition, now there is no arch entry in the bios boot and the re-installed arch was booting before you did all this. If so, it would seem that the arch bootloader was copied over somehow. Did you use a live iso for this? I don't see anything wrong in the picture you posted, but then again I don't know the partition layout or anything else about the system.

thats right, i used LiveOS Arch for the file copy stuff.

sda3 is the partition where my Arch was.

It looks like you will have to use the LiveOS Arch to reinstall grub.

i tried reinstalling GRUB by following this small guide https://sangams.com.np/how-to-restor...in-arch-linux/

below is disk with arch
https://ibb.co/dJHSxS7

below is how far i came and where it stopped.
https://ibb.co/7S577dv

any idea how to get it working?

What about copying those small lines between code tags ? Would be easier for people who want to help…

What does the next command says ?

My guess is it might show some EFI directory…

you need to create the directory /boot/efi before mounting the efi partition.

What makes you think I am trolling?!?

There is no Arch in BIOS, ever.
The photo doesn't show the BIOS or the missing Arch. It just shows how you are trying to recover your home filesystem.
My suggestion is to fix your bootloader. Others suggest the same thing.

i succesfully reinstalled GRUB and after boot i get this https://ibb.co/C9qDdnx what have i to do now?

From the link in your #7 post.

well, thats what i did aswell but here, i just did everthing again as you can see in the pic https://ibb.co/XJwbpP0 and then after this i used and i still got only the grub like here shown before https://ibb.co/C9qDdnx

chroot into your arch system post the output of

Did you mount the efi partition to /boot/efi before running the grub-mkconfig?