/home/etc

It is a backup directory owned by root. The reason is that it sits in the partition that is preserved, and it is outside my user folder, because it is better organized that way.

Those are equivalent.

No. ~etc is equivalent to /home/etc. ~/etc is the same as /home/<current user>/etc.

On most systems, that is not the case. Typically a user's home directory is `/home/USERNAME` so `~/etc` would be `/home/USERNAME/etc`.

Try it for yourself:

[ /home/etc = ~/etc ] || echo theyre different