Is the contract granting David Pecker's immunity in the current
criminal trial of Donald Trump public?
I don't know. It may even have been a purely oral promise made on the court record and not memorialized in a written agreement. This wouldn't be particularly uncommon.
But, in all probability, Pecker didn't have a choice.
If the prosecutor unilaterally grants you with the constitutionally required "use immunity" from criminal prosecution, you are no longer entitled to refuse to testify based upon the Fifth Amendment to the United States Constitution (as incorporated against state governments via the due process clause of the Fourteenth Amendment to the United States Constitution). Instead, you can be compelled to testify by subpoena whether you want to or not, once the prosecutor provides you with use immunity. As explained at the link:
The Fifth Amendment of the United States Constitution provides the
right against self-incrimination, which means a person cannot be
compelled to testify against themselves in a criminal case. However,
if a person has relevant information that is important to a case, the
government may offer them immunity from prosecution to obtain their
testimony. The landmark case of Kastigar v. United States, 406 U.S.
441 (1972), established the principle that immunity agreements
must provide "coextensive" protection to the witness to prevent any
derivative use of their testimony against them.
So, if a criminal prosecution was developed completely independently of the compelled testimony for which Pecker was granted immunity, Pecker could be prosecuted for crimes that he testified about.
Also, which "fruits of his testimony" can't be used to develop more testimony, this constitutionally permitted balance isn't perfect for criminal defendants. This is because even the vague knowledge based upon his testimony that he did commit a crime, which probably isn't specific enough knowledge of his testimony to bar his prosecution in another case, still helps prosecutors a lot. It does so by making it possible for them to ignore leads suggesting that other suspects committed the crime or that a crime was not committed. Knowing that an answer is out there can be helpful as a practical matter, even without knowing what the answer was or where it came from.
So, just considering criminal cases, for what crimes does Pecker have
immunity? in what jurisdiction? For example, could Pecker have
murdered one of Trumps' enemies without criminal consequence from any
USA government body?
The immunity provided is only immunity from the use of that testimony or the fruits of that testimony to prosecute him for a crime. Pecker is not immune from being prosecuted for any particular crimes. He merely has "use immunity" to prevent his testimony from being used against him.
Pecker's testimony can be used against him in civil matters. The prosecutor does not have the authority to provide him with immunity from civil lawsuits based upon his testimony.
I believe that this use immunity protection would bind any other U.S. federal, state, or local jurisdiction that wanted to use that testimony in a criminal prosecution, but I have never personally researched that legal question.
The issue would probably be framed as one of whether Pecker had voluntarily waived his 5th Amendment rights, which would probably not be the case if he testified pursuant to a subpoena and was not allowed to claim the 5th Amendment due to a prosecutor's unilateral grant of use immunity. In other words, used of his testimony or fruits of it would probably have a treatment similar to a confession obtained with a Miranda violation.
