How do you stop the tiny parts from sticking to your soldering iron tip?

The sticking-to-the-tip thing almost always means you're touching the iron to the part itself instead of the pad. What worked for me: tin one pad with a tiny blob of solder, place the part with tweezers, then hold it down and touch the iron to the tinned pad only, not the component. The solder reflows and grabs the end cap without the iron ever contacting it. If the tip has any residual solder on it, wipe it on a damp sponge or brass wool first, because even a small bead will want to jump onto the part. And go easy on that first pad. If there's too much solder it bulges up and the part slides sideways right off, which sounds like your second problem. A thin film is all you need, plus a decent dab of gel flux. Liquid flux from a bottle tends to run everywhere and can actually pull the part across the pads as it wicks. For the second side, feed a little wire solder at the pad edge and let it flow under, again keeping the tip on the pad land rather than the cap.

If you keep fighting it, honestly the easier route for tiny passives is to skip the iron-on-the-part approach entirely. Dispense a small dot of paste on both pads, place the part with tweezers, and hit it with hot air or a cheap hotplate until it reflows. Surface tension does the alignment for you and self-centers the part. That's how most of these practice boards were meant to be done anyway, and it's way less frustrating.

On magnification, a headband magnifier is fine for through-hole and big chips, but for the smallest passives I couldn't judge joints at all with one either. A cheap USB microscope plugged into a laptop got me by for a long time. Eventually I picked up a secondhand stereo microscope and it's a different world, but that's a bigger spend and overkill if you only solder occasionally. The USB scope is the sweet spot for checking your work after the fact, even if you solder looking through the magnifier.

One thing that helped me alot with those edge columns was flooding both pads with solder first, then dragging a wick braid across them to pull the excess off, which leaves a thin, mostly flat film that's actually the right amount for tacking. It sounds backwards to add solder just to remove it, but it beats trying to feed exactly the right tiny amount by eye. Also, on tip geometry, I found a small chisel tip far more forgiving than the needle-fine one I started with, since the fine point dumps heat into one spot and makes you want to stab at the part. Did you check what tip you were using, out of curiosity?

The tip sticking thing happened to me too and turned out my hands were shaking, the tweezers would drift and bump the part while the iron was still on it. Now I rest my elbows on the desk and anchor my wrist against the board edge and it mostly stopped. Also I noticed my joints looked way better after I stopped rushing, like give the pad a second to actually melt before you pull away.

One thing I keep wondering about, does the temperture setting matter much for those tiny parts? I just leave mine somewhere in the middle and have no idea if that's right.

Back before hot air was cheap I did all my little parts with a tack-and-solder method and a loupe from a pawn shop, couple bucks and better optics than any headband rig. One more thing on judging your work, don't go by shine. With lead-free the joints always look dull and gray anyway, so I judge by shape instead, the fillet should climb the end cap a little like a ramp. If it sits there like a ball it never wet properly. And if you end up reflowing the same part a dozen times, let the board cool down between goes, cooked pads lift easy.