Having a bit of a wet steam, I wanted to check the level probe on my Izzo Vivi.
The outer nut can be screwed off, but the teflon "tube" is so stuck I am suspecting I cannot remove it without damaging it or worse; have half the part drop into the boiler.

Just read this thread stating that the outer nut should be loosened, but this is part of the boiler, and cannot be loosened...

Vetrano Boiler Fill Solenoid Issue?

I cannot pull the probe wire itself all the way out, so I just lowered it a bit, to try and force the filling to stop earlier.
But after I tightened the nut the probe itself can still be rotated a bit. Not loose but not unmovable either. Is this normal?

Yes, it's normal for the probe to swivel. It's been a while since I had my Duetto but, iirc, once you completely loosen the upper nut, you just pull the Teflon piece and probe out together as a unit. I imagine the Vivi is built the same. I suggest buying a spare probe assembly, then once you have that, loose the nut until the threads are completely unengaged, then grab the Teflon below the nut with pliers and pull upwards to remove the entire assembly. If your Teflon is ok, reuse it. If not, you'll be glad you have a replacement on hand. The old probe can be polished and reused if you want to.