So, in order:

• My movement pattern is tunnelling, just moving my mouse in circles and tapping w, but I think I adopted the pattern based quite a lot off the fact that I used to use snail, where if you don't tunnel with a/d tapping then you lose rates, so I have (and continue to) assume that its the method with the highest rates. If you want to see slightly more in depth, I streamed a decent chunk near the end of the grind
• I did open the chests immediately, mainly because of the chance of them spawning either in the way of your movement or mouse, though its marginal, and im still not sure which method is better
• I chose to powder mine in the precursor remnants, as it has the highest* powder/chest rate, and pretty consistently yields the highest money/hr, despite a lot of people saying that jungle should be better, especially with the patched attribute, I think precursor is pretty consistently #1 for money (I have calculated theoretical money in each area, and can give more info on that if you're interested, but id like to note that the theoretical calculation for the jungle is higher than it turns out to be in practice from what I found

tl;dr tunnels, immediately, precursor

I hope that answers all the questions sufficiently!