Generally it's just
- Upload new parent theme directory to
- Upload new child theme directory to
- Activate child theme
If that doesn't work activate the old theme. As long as you are uploading to new directories and not overwriting anything then you'll be fine.
Make a full backup beforehand if you're really want to play it safe.
Do I change the address in General settings before moving the template folder?
You're just changing the theme, so the general settings will remain the same.
Will the SEO settings remain the same?
Now THAT I have no idea. I don't see why it would change but alphabet soup was never my thing. ;)