I do, maybe about once a year. My Cochin boys (and the Silkie boys) get super weird spurs that curl instead of growing out, so in their case it's more to prevent their spurs from growing into their legs than anything! I'll take the sharp point off of the OEGB boys' spurs just in case if they start getting feisty, though, and trim them if they get to be too long and are a danger of tripping them up or something. You can usually see where the quick is in them because of their light skin, so just be careful to avoid that when you snip. I just use dog nail trimmers for mine, though I've heard of using a dremel for the job as well.
Ah, bittersweet, but I'll bet it's much more peaceful out there without him harassing everyone.
Popcorn does look quite tall for a Cochin in that picture! Since he was a feed store baby, he's most likely just hatchery quality, which often differ from the proper breed just a little bit in some way or another.
Sometimes, yes. Not all the time and not every one of them, but with more frequency than birds with less fluffy butts in my experience. What I do when they get like that is I just take a set of scissors and trim it out. Usually trimming the poop out shortens the feathers enough that it doesn't get as bad again, at least until they molt and the feathers regrow. I do it on my own, but if you have someone to hold the bird while you trim, it goes a lot faster. Just be careful if you need to trim close to the skin or vent on any of them!