ZRJ '00 Cherokee XJ

Hey guys. I'm very new, but trying to learn and I need help.

Have a '00 XJ Sport.

Today I noticed some wispy blackish grey smoke coming from under the hood when I stopped at the store on the way home.
I didn't have time to look, but when I came out it was gone. Didn't see anymore and made it home with no issues.
I popped the hood and ran it in idle with the hood up watching for anything.
Here's what my untrained eyes and ears detected.
The fan on drivers side called "Fan Module" on a breakdown I saw online wasn't spinning. Should it be? I don't think its the radiator fan.
Second, I heard something from passenger side (it sounded like) clicking like it was trying to turn something on. Happened every 10-20 seconds or so. May idea what that is?
Only symptoms leading up to today are our roads are extremely rough so the Jeep is constantly shaking hard and I noticed something vibrating like a shuddering of sorts that sounded like it was coming from under the hood. I don't know for sure where it was because it only happens when I hit a hard bump.
I know it's really generic, but any ideas where to start looking? And please assume I know nothing. I'm learning as I go.
Oh..all gauges are normal.

Sass

Stabsthedrama

The auxiliary fan will only start when the engine reaches a certain temp, you'll hear/see it turn on, especially if you sit idle for 5+ minutes on a warm enough day (these commonly go bad, so I would check this if you're unsure if it's starting up or not) - I've had to rig one up to my ignition on my last 96.

As far as "smoke" I would have to know where from...the back of the valve cover like back where the exhaust is, possibly burning off the exhaust? out of the top of the valve cover?

As for the "clicking from passenger side" - are you running (or trying to run) the A/C? Also, see if you can isolate it to the relay area, since it certainly could be a bad relay/electrical issue causing a relay issue (you shouldn't hear them normally)

As for the shuddering on hard bumps, this again could be a lot of things - from a loose starter or other parts to bad engine mounts, could be a whole lot of things...

More info would help us a lot.