You can stitch together the Perseverance launch operations flow from online photos. But first, to answer your questions:
At what "altitude" did this happen, and what happened next? It happened at the top of the rocket, something like 50 m above the ground.
Did Perseverance get put into the fairing and the fair get closed up on the ground level, and then a crane lifted the sealed fairing up to the top of the rocket, or is the mobile clean room "at altitude" near the top of the rocket and everything happens up there? Perseverance was encapsulated in the fairing at ground level in a separate clean room, some miles from the launch site. It was then trucked to the Atlas V vertical assembly building and hoisted to the top of the rocket. A temporary "mobile clean room" was set up at the top of the rocket, inside the building, and the MMRTG was installed inside the mobile clean room.
So back to our story: The rover arrives at the Cape. Note that the MMRTG has not yet been installed. There is a cage-like structure at the rover's far end waiting for it.
Here's the rover already integrated with the backshell. You can tell you're looking at the bottom of the rover because the red rocket engines are facing the viewer.
The fully integrated spacecraft about to be encapsulated in the Atlas V fairing. The heat shield is at the top with the backshell below it, together forming the entry system. Note the hatch in the backshell - that's where the MMRTG will be installed. Below the entry system, barely visible, is the cruise stage. The blue panels inside the fairing are intended to absorb the noise of launch.
After encapsulation, the fairing assembly is trucked to the Atlas V launch site and hoisted to the top of the rocket.
The MMRTG gets hoisted up to get installed on the rover.
This is a practice MMRTG installation back at JPL, but it gives you an idea of how it's supposed to work...if there weren't a fairing there, anyhow.
The real MMRTG, way up by the tip of the rocket.
And installed in its handling fixture at the right angle to mate with the rover.
I didn't find any pictures showing the actual MMRTG installation or the mobile clean room.
Finally they rolled the complete system to the launch site:
BTW, this "mobile clean room" sounds like an perfectly ordinary clean tent like this one, but bigger and probably fancier: