Could you have committed an unrelated murder, and by disclosing this murder in your testimony, become immune to conviction of it?
If that is not how immunity works, then how can the government force anyone to testify? The government does not know what (unrelated) crimes I may have to confess to in order to give truthful testimony on the matter in question.
i'm not even sure what the answer to this is other than to say -- it's a completely contrived example and there's no way you would answer such a question let alone be asked about it. getting on the stand isn't some grand fishing expedition -- you're asked relevant questions and if they're not relevant then your lawyer / opposing lawyer is going to challenge relevance
If you explicitly have immunity for all things you reveal in the course of the questioning (and that immunity applies to the crimes revealed, not just that particular testimony), then I don’t see why you wouldn’t reveal everything you can, whether asked or not. Any way you could possibly shoehorn “I murdered a guy in 2012” into an answer, you should, if that were how the immunity worked.
If that is not how immunity works, then how can the government force anyone to testify? The government does not know what (unrelated) crimes I may have to confess to in order to give truthful testimony on the matter in question.