So every time I render and animation scene using iRay with iClone 7, the progress bar stops at 1% for hours. Clearly, there is something wrong. Has anyone else experienced that?

Ouch.
This can be tough to solve.  So many little details that can clog the plumbing.  Just have to find the needle in the haystack.

What is your GPU?
Does the Iray "preview" work okay?
Have you tried rendering Iray on more than one project?  A very, very simple one?
How many frames are you trying to export?  (Maybe try a 10-frame sequence.  Or 3.)
When "rendering," is your CPU busy?
Same question for your graphics card, is it busy?  I recommend the free utility GPU-Z ("G" as in "graphics") to monitor your video card activity.

It could also be possible that reinstalling the Iray plug-in will help.

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iClone 7... Character Creator... Substance Designer/Painter... Blender... Audacity...
Desktop (homebuilt) - Windows 10, Ryzen 9 3900x CPU, GTX 1080 GPU (8GB), 32GB RAM, Asus X570 Pro motherboard, 2TB SSD, terabytes of disk space, dual  monitors.
Laptop - Windows 10, MSI GS63VR STEALTH-252, 16GB RAM, GTX 1060 (6GB), 256GB SSD and 1TB HDD

My GPU is a GeForce 1080Ti 11gb, a Ryzen 5 3600 CPU, 32gb or G Skillz RipJaw V ram and a ton of HD space. I have Windows 10 Pro, 

iRay preview works just fine. I haven't tried a simple project yet.

I tried exporting 200 frames. I actually deactivated the CPU and just let the GPU render.