3) The reason the potentiometer base doesn't fit well is because of the pin shapes. They're metal strips that measure 1.05mm wide and .29mm thick at the breadboard end, but this thin shaft is only 3.9mm long at which point the width broadens to 1.98mm. I do not have a tool to measure the breadboard holes; that wider shaft doesn't fit in the hole but the length of thin shaft isn't long enough to make contact unless you push it down hard.
Presumably I need to solder header pins onto the ends to make it work as intended. I don't have the first clue about soldering, anyone throw me a bone?
You can actually fix it very easy without soldering. The reason the potentiometer doesn't fit well is that the holes in the breadboard are actually not round, but slits. The slits are horizontal, whereas the male pins of the potentiometer are vertical. If you take a small plier and carefully rotate the thinner bottom half of the potentiometer pins by 45° they will fit nicely. I just came across this while doing Project 05 of the starter kit. Honestly, I think these minor misalignments are part of the beauty of the kit, it's you are working with off the shelf components, not with something 100% pre-baked for you.