SuperDuper! doesn't clone the Recovery partition to the target drive, so no, you won't find one there, though it will still be on the drive you were cloning from.
1. It's a fairly simple way to reinstall the OS if you have no other means. It still does take almost as long as downloading the OS from Apple's servers through the App Store since most of the reinstall from the Recovery partition is also done that way.
You'd be much better off purchasing an 8GB flash drive and making your own Mavericks installer. Download Mavericks from the App Store (if you didn't save a copy of it). When it's done downloading, it will want to install. Press Command+Q to stop the installation. Then use DiskMaker X to create a bootable flash drive. Everything needed to install Mavericks will be on the flash drive, so it will install significantly faster since you don't have to wait for any part of the OS to download. You can then delete the Mavericks installer from the Applications folder.
2. Basically, yes. You can just boot to the backup and clone it back. Then all of your apps are already installed. All of your settings in place, etc. The only data you'd lose is anything (emails, documents) that hadn't been backup up yet since the last clone.
3. Yes, login to your App Store account and click on Purchases. Mavericks should have a Download button next to it.