3TB Fusion is now a 121GB Flash Drive after reinstall

First, a Mac cannot install and run a system older than itself. Your iMac if it is indeed a late 2012 model came preinstalled with Mountain Lion 10.8 which did not ship on disc. I'm guessing your iMac is older than 2012 even though you may have purchased it that year. It would be helpful if you would look at About this Mac under the Apple menu and tell us what it says.

Secondly, it sounds like the 3TB HDD has failed leaving only the 121 Gb flash storage part of the fusion drive available for install. I recommend making an appointment and taking your iMac in to the nearest Apple Store or AASP for a proper diagnosis and estimate of repair.

I agree with the above comments that it sounds like the 3TB hard drive that is part for your Fusion Drive was probably failing which caused the slow performance issues you described. I suggest running the Disk Utility application location in the application/utilities folder to see if it is able to see and test (First Aid) the hard drive. I suspect it either won't wee the hard drive, or if it does it will likely generate some errors when you run First Aid. You can also download and run Etrecheck which also reads and provides the ability to display the storage device SMART logs which if errors are present may indicate that your hard drive should be replaced before proceeding any further. Hopefully you've been maintaining regular backups of your data.

If the hard drive is OK, then you may want to seek help in restoring your Fusion Drive so that the hard drive and flash drive once again work as one logical unit. You can find the instructions online by searching using terms like "terminal command to fix fusion drive", however unless you feel comfortable using the terminal application then I would suggest contacting Apple or other trusted support personnel for assistance.

Your iMac is running a version of OS X that isn't supported, Lion. Restoring OS X on it does not require disks. Here's what you should have done:

Clean Install of Sierra or El Capitan on a Clean Disk

1. Restart the computer. Immediately after the chime hold down the Command-Option-Rkeys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the drive (usually, the out-dented entry) from the side list.
5. Click on the Erase tab in Disk Utility's main window. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to Mac OS Extended (Journaled.)
8. Click on the Apply button, then click on the Done button when it activates.
9. Quit Disk Utility and return to the Utility Menu.
10. Select Install OS X and click on the Continue button.

This should install the version of OS X that was pre-installed when the computer was new. You can then download Sierra and upgrade.

Yes, it knows which OS version to install. Although you haven't provided information from Disk Utility, the HDD may be failing or has failed.