If site1.local is accessible from my.domain.com you probably have dns multitenant disabled. As long as you intend to run only one ERPNext, this will be fine.
I recommend to restore the database into the same version and then upgrade so that the patches are applied. Otherwise, you might run into issues such as Column 'translatable' cannot be null
The backup will export one site per run. It will be the site, in which folder you find the backup. On restore, define the site to restore to
$ bench --site my.domain.com backup
$ bench --site site1.local restore