Nothing on number 1 Steve. Number 2, I have heard the same thing. Do you have any source on that? If so, I could use it as a footnote at least.
Apologize to Fred for diverting this from his topic/subject. Maybe I'll start a thread but it's probably too obscure to do so.
On #1: Epstein gives no footnotes on it. It's a passing sentence.
On #2: It's the Setyaev interview, the Radio Moscow matter. You list it in the timeline.
Two quick points on it: When Oswald was on the ship returning home he wrote a series of imaginary questions and answers for the press that he expected to meet him. In answer to one question, "Did you make statements against the US there?" he wrote: "Yes, I made a recording for Radio Moscow which was broadcast the following Sunday in which I spoke about the beautiful capital of the Socialist work (sic) and all its progress." Epstein said he later revised the (draft) answer and said he only talked about the "interesting places" in Moscow that he visited.
In the FBI's Gemberling Report: Marina was interviewed on September 8, 1964 and they asked her a number of questions about this alleged radio broadcast.
Briefly: Marina said Oswald tried to contact Setyaev later and she asked why, who was this person? He replied that "He was a man who helped him make some money shortly after his arrival in Moscow by assisting him in a broadcast for Radio Moscow. Marina asked Oswald what he had said and he told her he had criticized the United States and said Russia was a better place in which to live."
https://www.maryferrell.org/showDoc.html?docId=11941#relPageId=228Epstein gives more details on this too. See his endnotes on the chapter.
As you stated, McMillan and others think it was the KGB sniffing Oswald out. There was no actual broadcast done of the interview. But Nosenko said he never knew about the matter and none of the KGB agents Mailer and his people interviewed (in "Oswald's Tale") mentioned it either. I would think the US would be have been monitoring Soviet radio and any interview with him discovered?
Best guess: a recorded interview did take place but it wasn't broadcast.