The backups you made were done with an Asus app and you need that exact app to restore those backups. You have nothing Asus left on your tablet except the hardware and bootloader. Those apps do not run under Katkiss, they are hopelessly outdated. Plus, you should never, absolutely never, restore backed up apps from an earlier Android version to a new rom. It causes nothing but trouble.
Go into the Play Store to My Apps. If you are using the same Google account your apps are all there.
While you are there search for a file manager. there are tons of them.
If you liked the Asus file manager you might get lucky and see the Asus Zen UI file manager there. But there are many other choices and the Asus manager is very very basic. ES File Explorer is good (if you like it, get the paid version - it's worth it), many people like Astro, I like File Manager HD... FX Explorer is good.... Download a few, test drive them and keep what you like best.
The "reference material" for your new rom is the thread you downloaded it from. Read it! Lots of good information there. But you just got a pretty amazing piece of software that turned your ancient ICS POS into a usable and (almost) up to date tablet FOR FREE. We prefer our developers, who do all of this work in their spare time with no pay, to keep developing instead of writing manuals....
It's up to you and your skills with Google search to unlock the potential of your new machine.
And then there's an amazing community of people here and on XDA to help you out. But we do expect you to make an effort first