This is not something you can restore, because auto-mounting is a non-persistent process. If however you set up those other filesystems in /etc/fstab or by way of systemd mounts, then that information will be copied over when you copy back the /etc of your original system.
For educational purposes, I will also include the following tutorial… 
Same as above. This will be configured under /etc and will thus be copied over again with the commands I gave you higher up.
Themes and wallpapers are stored under your $HOME, so they will be copied over alongside the rest if you execute the commands as I showed you higher up.
Login screens are a different thing. The splash screen that you see — if enabled — after logging in is also stored in your $HOME, but the actual login screens are a system-wide thing, and would need to be reinstalled from where you got them.
This should normally be copied over with the commands I gave you.
Well, I am not a gamer and I’ve never used Steam, but I suspect that those games will be in a directory ~/Steam or something of the likes. So you will have to look for such a directory in your old home directory on the broken drive, and then copy it over. You should be able to do this from within a graphical file manager such as Dolphin.