You're mistaken as to what prosecutorial immunity is and what it means. Prosecutorial immunity is a hybrid of judicial immunity, whereby prosecutors have absolute immunity when acting as an officer of the court in their capacity as an advocate (lawyer) for the state. After probable cause has been established, the "proceeding" phase is said to have begun, and from that point through verdict he prosecutor has absolute immunity. In an investigative or administrative role (essentially prior to the point at which probable cause exists, there is qualified immunity. So, the questions you ask have nothing whatsoever do do with prosecutorial immunity.
Taking your questions on their face and ignoring your classification of the issues, I will go in order:
Suppose I commit a murder of a federal official (anyone?) and get away with it. Later I discover that some other unfortunate individual is being prosecuted for the murder I committed. I feel sorry for him, so I confess to a lawyer and wonder if I can do anything to get the innocent defendant free.
Can my lawyer communicate anything to the prosecutor (or defense counsel) that would cause me to be subpoenaed, at which point I would invoke my fifth-amendment rights? Can this be done in such a way that the prosecutor would absolutely move the court to compel my testimony under immunity?
Your lawyer can only reveal what you communicate to him/her with your explicit written permission, and a confession would really be the only way to help the "unfortunate" innocent you feel sorry for. If your lawyer breaks confidentiality without your permission, not only will he or she likely be disbarred, but the information would not be admissible as it is protected by attorneys-client privilege, and therefore you could prevent the testimony from being proffered in any action. You would not need to invoke the 5th Amendment as you (your new lawyer) would have any subpoena quashed based on the privilege (of course in the real world this would never happen).
Suppose I have been given prosecutorial immunity. Now I provide testimony that exculpates the defendant and implicates me beyond a reasonable doubt for a number of crimes in multiple jurisdictions: murder subject to both state and federal prosecution, as well as other felonies related to the commission of the murder that would have never come to light but for my testimony. Am I truly immune to prosecution for any of those crimes in any U.S. jurisdiction?
No. When a prosecutor drafts/offers an immunity agreement, it is only for the jurisdiction over which they have the power to grant it. If the federal government or another state has the ability to bring charges, that cannot be bargained away by another jurisdictions prosecutor. Not only that, but when a prosecutor enters into an immunity agreement, it is never to help exculpate an individual already convicted of murder - they wouldn't offer immunity for this - this just isn't how it works. In fact, if you walked in and confessed to the prosecutor themselves, it probably wouldn't be enough for them to reopen a conviction. They nearly always have multiple pieces of evidence when they go to trial, so if anything, they would try you as a secondary defendant, but wouldn't just take your word for it that the person a jury already convicted is innocent.
Immunity agreements typically arise when there are multiple suspects/defendants and they offer a deal to the less culpable to testify against the other. The agreement will say something like "this is how we think the crime went down. We want you to tell us exactly what happened and agree to testify against the (other) defendant. Assuming your culpability is no more than X (say an accessory) you will get immunity from prosecution for anything you say". It will explicitly say something to the extent of "if you testify to crimes beyond which we are offering your immunity, this statement can be used against you". There are never blanket immunity agreements where the person given immunity can turn around and confess to any and every crime, or say, "I'm actually the one who committed the crime your asking me to testify about". If that happened, you would be prosecuted. Unless you lied and your lawyer had no clue, he/she would never let you say that anyway. When a defendant enters into an immunity agreement, your attorney would go over, ad nauseum, every single word that (you) the defendant will say prior to it being offered to the prosecutor.
But now aren't I subject to civil liability? E.g., the family of the victim would absolutely win a judgement for Wrongful Death. How is it justifiable for a court to compel me to give evidence that will ultimately impoverish me, even though it does not result in my incarceration? Or is there some protection against this sort of collateral damage?
This would be the least of your worries, but yes, a conviction for murder is absolute proof of wrongful death since the burden on proof for the tort is only a "preponderance" and for a crime its "beyond reasonable doubt". The judgment would carry over and there would only be a trial on damages; liability is already established. There are no protections and the court is requiring you to do anything. You are doing it, in this hypothetical, of your own volition.
