I am aware that members of Congress have some immunities and so do the President and Vice President, but what about Supreme Court justices or federal prosecutors for example?
Members of Congress are immune to arrest during sessions of Congress and on the way to and from sessions. They have immunity for legislative actions. Article I section 6 says in relevant part:
They shall in all cases, except treason, felony and breach of the peace, be privileged from arrest during their attendance at the session of their respective Houses, and in going to and returning from the same; and for any speech or debate in either House, they shall not be questioned in any other place.
The Justice Department has issued an opinion that a sitting President may not be indicted. This has not been tested in court.
Judicial Immunity protects all judges from being sued for their action in the course of judicial duties.
Prosecutorial immunity means that that prosecutors in the United States cannot be personally sued for a decision on whether or not to prosecute a give case, nor for how that case was presented, even when there was clear misconduct. Thius was set out in Imbler v. Pachtman, 424 U.S. 409 (1976)
Government officials generally have Qualified immunity when carrying out their official duties. This prevents them from being personally sued for their official actions.It was first defined in Pierson v. Ray, 386 U.S. 547 (1967) It can be lo9st in various circumstances, particularly if the acts were contrary to "clearly established" law, and the official should have known that. The current standard set out in Harlow v. Fitzgerald, 457 U.S. 800 (1982) is:
[G]overnment officials performing discretionary functions generally are shielded from liability for civil damages insofar as their conduct does not violate clearly established statutory or constitutional rights of which a reasonable person would have known.
Qualified immunity has mostly been applied to the actions of police officers.