RE: first print trash; extruder "clicking" noises
Did you loosen all six M3 screws (3*2) which old the three trapezoidal nuts at once? The lateral position of the bed should be defined only by the two smooth rods. The nuts need to settle into matching lateral positions, to avoid strain in the Z drive.
At first, I only reset the rear one. Then I removed all 6 to run the nuts up the rods and back down. They seemed fine. I made sure the screws were re-tightened while the plate was at the very bottom. I also ran the z-axis alignment calibration to make sure everything was lined up properly, and then the z-axis test again.
Also, many kit builders have found that they need to lubricate the lead screws to avoid noises during movement. The squeak you get towards the end of the Z range is pretty unique, but groaning noises during longer Z travel are not uncommon. Applying a bit of the lubricant that came with the kit has fixed the noise in all cases I have followed here on the forum.
I added some lubricant and it seemed to fix most of the noise, but I can't get the z-axis test to pass. There's nothing visually obvious that I can see. The plate moves up and down the full range and stays level the whole time.
I have noticed a couple of times that when I first power the printer on, and I go straight to the manual z-axis movement option in the menu, the printer seems to be confused about where the plate is. I have to run the z-axis alignment calibration, and then the manual z-axis movement from the menu behaves normally.
I still can't get the z-axis test to pass, however. It passed at least once before I attempted the first print (which went poorly), but I can't figure out why it's not passing now.
RE: first print trash; extruder "clicking" noises
It is normal that the Core One forgets its XYZ positions when powered off. You do not need to run the "Z alignment calibration" in that case (where the bed moves down to the mechanical end stops), only the "Auto home" (where the bed moves up until it reaches the nozzle's load cell). The printer will also do the homing on its own before a print.
If the Z axis test fails, it might not be related to the mechanical Z drive at all, but could also be due to problems with the load cell sensing. A somewhat common and easily fixed cause seems to be that the nozzle is not inserted far enough into the hotend. There should only be a gap of ~ 2mm between the heater block and the brass part of the nozzle, as shown here.
RE:
Thanks for the hint about the calibration. That's good to know.
Because it's taken from an angle, I can't tell from the photo you linked the actual vertical distance that the nozzle is supposed to be. Edit: sorry, I completely missed the inset photo. However, that inset photo makes it look like the red/orange ring is way, way higher than mine could possibly go - as if the red/orange ring itself is pushed up and into the extruder assembly?
The big orange arrows just point up. without any real reference to how far. I've attached a photo of what mine looks like right now. It's too small of a space to fit into to measure with calipers (the only metric tool I have), so I'm not sure if it's 2mm or not. I attached a photo with a tape measure next to it, but it's in inches and I doubt it helps very much because it's the coarse side.
I think my first print may have been messed up, at least in part, because the nozzle was too far down. Since then and finding out from there that I needed to raise the nozzle up, I can't get this z-axis test to pass. It's impossible for me to know for sure, but it _seems_ like the load cell test is maybe also a little more difficult to pass now. I don't have to strike the nozzle hard, but I do have to tap it with my finger fairly firmly to get the test to pass. Touching it on command (even though the little horizontal bar on the screen registers) is not enough to pass the test. It may have been that way from the start. It's really hard to tell - and the screen doesn't show - if the z-axis test is actually coming into contact with the nozzle as it appears to be intending to do.
I don't know if that's part of the problem and why the z-axis test won't pass. It seems reasonable that this would be a way to sense that maybe the plate is at it's highest position. Unfortunately I can't seem to get any diagnostic information from the printer other than the test fails.
RE:
If the Z axis test fails, it might not be related to the mechanical Z drive at all, but could also be due to problems with the load cell sensing. A somewhat common and easily fixed cause seems to be that the nozzle is not inserted far enough into the hotend. There should only be a gap of ~ 2mm between the heater block and the brass part of the nozzle, as shown here.
The inset image was the key. Finally got a print. I don't know if I feel relieved that it finally worked or like I accomplished something. Maybe both. To push the nozzle up that far you have to push through some spring tension. It's not much tension, but it's enough that it didn't seem like it wanted to move that far up into the extruder assembly.
With the nozzle pushed further in, the z-axis test passed easily and the load cell test seemed (it's difficult to tell) to take much less force to pass as well.
Thanks for everyone's help and patience while I figured this out.
edit: thanks @hyiger. I should have paid more attention to what you were telling me and I would have figured this out two weeks ago.