1. Is there any canon reference for what happens when someone with preexisting cyberware gains the regeneration power, for example as a result of being a spirit's hidden life? Is the cyberware immediately pushed out, does it remain, is it only destroyed if the regeneration kicks in?

2. Let's say someone like the person from the above question takes a deadly wound (for sake of simplicity) and fails their regeneration roll. Are they then really dead dead? (Seems nonsensical, but some people claim it's what the rules say.) Or are they just bleeding out into overdamage like anyone else would be?

3. Do you or your gaming group grant instakills for shots to the brain of a regenerating being, or does that just mean that they have to roll above 2 instead of above 1 on their regen roll? Canon seems a bit confused on this point, so I'm curious what people do.

1. The Shadowrun Companion makes it a point to exclude cyberware from a regenerating character. Page 37 covers it, and mentions "the cyberware is usually purged from the body in a particularly messy -- and painful -- fashion soon after" when the "next to impossible" surgery is successful.

2. Same book, page 36. "On a result of 1, the shapeshifter does not regenerate, and may die if they do not receive medical care per standard rules. They're just bleeding out into overdamage like anyone else would be.

3. They have to roll regen, just like usual. I'll take your word that there's confusion, but I can't find anything that contradicts.

1. The companion's reference there is to installing cyberware in shapeshifting characters, who presumably have the regenerative capacity before the surgery is done (hence the near-impossibility). I'm asking more about characters who already have cyberware, then gain regeneration. My instinct is that characters that paid for cyberware with essence don't automatically purge it; I've heard vague reference to a canon vampire with active cyberware, but I'm not sure if that's even 3rd ed.

There is no explicit statement about vampires and pre-existing cyberware. An old run book has an NPC that is a vampire with cyber (I think, could someone name which book?) and there has been no statement confirming or denying the normalcy of such an individual.
By the books, it is possible for a regenerating character to have cyberware. Whether this is the rule or exception is unstated. I am curious how implants would deal with mist form.

The module with the cybered up vamire was the NPC Nemesis from DNA/DOA. He was a cybered sammy/hitmal before he got infected. All his cyber kept functioning, but there would be no real way to repair it if it got damaged. No book rules has ever contridicted this in later editions, it was never addressed again.

His max essence as a vamp n 3rd edtition should then be his essence after cyberware x2.

To kill a regenerating character requires some critical injury to the spinal column (if I remember my Critters book correctly). The only "insta-kill" shot I would personally allow would require a certain amount of game flavor like:

"He's down and thrashing? I take my (edged weapon of choice) and hack his head off!"

or

"He's down and thrashing? I unload a fresh mag into his head until there's nothing but spinal column showing...then I grab my favorite bladed instrument...just to be sure."

Using the "called shot" mechanic would require a group agreement on what constitutes a called shot and the desired effect. Can a sniper irl put a round through someone's neck? Sure. Does the SR mechanic reflect that? Not at present.

The mechanic suggests two criteria: Massive damage to spine/brain (1 on a 2d6) or Massive overall trauma like being run over with a tank (2 on a 2d6). I submit unloading a full mag of EX ammo into a humanoid form constitutes "massive overall trauma".