I can't help with A and B, but I've observed the process twice. Once involved a pair of needle-nose pliars; the other involved removing the entire lock from the door. (In that case the door was unlocked but holding a broken key, which made it easier.)
Oh, and I tried removing the lock from the door, hoping to shake the key-fragment out, but I can't get it unscrewed! I'm not sure whether there's some trick I'm missing in the way it's mounted, or the screws just need a good soaking with WD-40 (which I know I have someplace, but can't find). (The screws that hold the lock mechanism can be unscrewed partway, at which point the lock slides back and forth about a third of an inch, but they stop turning at that point. If I knew the right name for the type of lock, I'd Google for information about installation/deinstallation of it.)
Cross-lock tweezers. + WD40? Never underestimate cross-lock tweezers. Dental pick might do. Do I need to go buy you pliers? I have plenty of small pliers. Wonky eyes are limiting, but love endures.
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Good luck!
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