Hi thanks for your writeup and questions!
1) This would be a GM call, but ultimately, if a piece of gear would remove risk (or significantly reduce it) then you can avoid rolling. Other times gear might just make it a bit easier (represented by rolling and discarding an extra die) or it might be that gear makes it possible at all.
For example, a grappling hook might make climbing easy enough that you don't need to roll, or there might still be some risk because you still have to avoid venting steam. But you won't be able to walk across the metal ceiling at all without MagBoots.
There is also an assumption that there would be more than one freelancer, each with their own set of gear. Playing solo you probably want to roll once or twice more for extra gear.
2) The intent was that Harm starts at 0, so you effectively get two free 'harm consequences'.
From my reading of your play-through, it looks like you were rolling a d6 for each zone on the way out against your Harm? The intent is that Harm Level is checked against when you roll for an action after the tower has fallen - either on your way out, or if you decide to push on upwards. So a HL of 3 has a small chance of being taken out (~3%) and that increases on a curve, up to HL 13, where any roll will be enough to finish you off.
So all things considered, you were probably playing on hard mode!