Would it be possible for me to create a completely new theme from scratch without a parent theme?
Ya, you can make one using the default theme and just edit it or make a test forum and make a theme on their.
Yes, go to ACP > Templates & Styles > Create New Theme and you'll get a new theme to work on...
How do you use that theme creator? It's really confusing...
It's just CSS, if you use the advanced mode, it's a bit clearer.