So the Russians have wiretaps they just presented to the FBI, of recorded calls between the Boston bombers and their mother, where it is apparent they were active in Jihad, or radical Islamic plans.
In the USA, unless there was a previous court order, wiretaps are not admissible (unless the Patriot Act fine print supersedes).
What about recorded calls from the USA that were wiretapped in Russia?
It would be illegal for the US to ask another country to do something the US could not legally do, but otherwise it’s fine.
An example would be that the cops can’t break in a house or ask a thief to break into a house to collect information, but if a thief broke into a house, discovered something illegal, and informed the police, then that would (usually) be probable cause for a warrant.
Illegally obtained evidence is admissible as long as the government didn’t request or encourage it.
but what if I illegally record a convo, to later use to support my case, in court. they won’t allow it, right? (even thou they - the govt - didn’t request or encourage me to record the call)
If you illegally record a conversation and attempt to introduce it in a civil case, it won’t be admitted. If you illegally record a conversation and the government wants to use it in a criminal action, the recording generally won’t be admissible pursuant to the statute that bars such recording. However, the government can have you testify about the conversation, and there’s no constitutional bar to admission of the recording (United States v. Jacobsen, 466 U.S. 109, 104 S.Ct. 1652.
As far as the OP’s question, there is a surprising amount of case law on the admission of evidence obtained by foreign sovereigns in a manner which would violate the US Constitution. Normally, it’s admissible: