Q: Move all iTunes library and backups to external storage

Not difficult, read here:

Manage and back up your iTunes media library - Apple Support

Two things to remember:

the first time you open iTunes after moving your Library: hold the Alt(option) key and point iTunes to where you have put the library on the external disk. iTunes will remember that.

When you want to use iTunes make sure that that disk is connected.

Lex

connect your iDevice to iTunes in your mac and sync.

take the songs from the backup (iBackupviewer).

or do it via iCloud.

You devices backups are in /Users/Home folder/Library/Application Support/MobileSync/Backup

so you could copy them from there. Whether they could continue to be backed up in the new location is the question.