Which parts effect the focus height adjustment? Is that done purely via the focusing mechanism, or does the articulating arm tilt up and down too?
There are a pair of knobs that adjust the magnification.
There is a knob that allows to to raise and lower the head, along with a tension knob ( Rack and pinion ).
You can change the eyepiece distances ( interpupillary distance ) and their individual strength ( dioper? ) I am an eye glasses wearer.
And of course the whole mechanism can be raised or lowered using the arm, there are knobs to set the
tension to keep it in place once set.
Once in focus it stays in focus when you adjust the magnification.
There's also a adjustment to tilt which you can lock in place.
How stable is it in the vertical direction?
To be honest I'm very happy with it and don't notice excessive wobbling.
But I do have a very stable work surface.
The best bit is how I can fold it away and keep the room I had on my desk.
I notice on your photo that you have placed the device under observation on a thick plate, which is elevated further by rubber feet or such. Hopefully that does not imply that the focus plane can't be moved all the way down to the bench surface?
I like to work on a piece of junk wood to avoid damage to the desk surface.
The arm can be raised and lowered very easily.
Also, If you find the camera is only looking at a tiny area of what you can see through the eyepiece then you may want to buy an adapter tube that's optically 1/2.
It will show a wider image on the camera.
It came with a 0.5 lens and another 0.5 for the camera

It is annoying that the cameras field of view is narrower than the one in the eyepieces but for the money I can't complain.
I'm soldering 01005 with it confidently...
It may tempt me out of my 0805 comfort zone

But I do just love those big parts right now.