How to diagnose suspect failing harddrive

My late 2013 27" iMac is failing quite spectacularly. I suspect the hard drive is dead (3TB Fusion Drive), but I don't know for sure if this is the problem, so wondered if there's anything I can do to verify exactly what's going on before I buy a load of kit to attempt replacing the drive.

• Symptoms are system wide hanging. Sometimes the spinning beach ball shows, sometimes whatever cursor is present when the hang starts. I can move the mouse cursor around the screen, but I can't click anything, can't change the focused application, can't swipe desktop spaces, can't bring up force quit.
• The hanging can continue for a very long time. Sometimes it ends and the system seems to return to normality, but very quickly afterwards it will hang again. Occasionally, but not always, there might be some weird visual artefacts - like parts of an app window disappearing, weird lines appearing, etc.

The above first happened just over a week ago. I was able to boot into recovery mode and using terminal I successfully moved essential data onto a USB drive. I ran repair disk in Disk Utility but this didn't repair anything and reported there were no problems with the drive.

I decided to completely format the drive and reinstall the OS. This has given me about 5 days of a usable Mac, but there were signs not all was right - occasional hanging for a few seconds here and there. Then this morning the above has happened again and it's completely unusable again.

My instinct tells me this is the hard drive, but I want to be able to confirm that before I buy a new drive and kit for opening up the Mac. Is there anything I can do to diagnose what's happening? Is it likely to be anything other than the Fusion Drive?

Thanks