"Program ran great, but it does not seem to have installed in Applications. It's still in Downloads."
Just "grab" it with the mouse and "drop it" into the applications folder.
Problem solved.
"If so, how can I access the backup I made to a Thunderbolt drive and "verify" the image? How do I test it's ability to boot the iMac?"
As another poster mentioned, you can use "startup disk" to specify which drive to boot from.
But there's also another way -- through the "startup manger". Here's how to use it.
1. Have Thunderbolt drive with your cloned backup connected and powered up - the drive icon should be on the desktop.
2. RESTART the Mac
3. As soon as you hear the startup sound, hold down the option key and KEEP HOLDING IT DOWN
4. In a few moments, the startup manager should appear
5. IF the Thunderbolt-connected drive is bootable, you should see an icon for it in the startup manager (along with the icon for your internal drive)
6. Click on the icon for the Thunderbolt drive to select it, then hit return.
7. If things are working properly, the Mac should now boot from the Thunderbolt drive (instead of from the internal).
IMPORTANT:
When you get to the finder, the Thunderbolt drive is going to look JUST LIKE THE INTERNAL, insofar as what you see on the desktop is concerned. After all, it's a "clone" -- it's supposed to be an exact copy of the original.
You can verify that you're booted from the Thunderbolt drive by choosing "About this Mac" right under the Apple menu -- it will indicate from what drive it's booted.
Another question you asked:
"Is there a way to have those external hard drive partitions icons not show on the desktop since I can see them in Finder anyways?"
You WANT to be able to see the icons for the two drives "on the desktop". (At least I do.)
You want to "know that they're there, and "mounted up" in front of you.
The fact that the Thunderbolt drive IS NOT there -- should tell you it isn't mounted. So you want to be able to know when it is.
I normally keep -7- drive icons mounted on my desktop, any one available at all times...