The data for the apps will be transferred automatically. It is captured in the backup. The apps should also download automatically in Step 4. Everything should transfer over including Notes, iBooks, Bookmarks and PDFs.
Yes, the data can be transferred between devices (based on what the device supports, like an iPad won't get Phone call data from an iPad backup).
An iPod Touch 7th generation can run iOS between 12.3 and 13.6, there are no differences in the restore process. The same older apps (generally 32 bit apps) will not run. If the iPod Touch 7th generation is restored, it will be automatically upgraded to iOS 13.6. If it is running an older iOS, and is not set up the restore process will use that version and yes you can upgrade later.