Game 6 scene, did that REALLY happened?

Yes, that really happened. It was also pointed out in the documentary "Bobby Fischer against the world".

Yes.
Fischer was surprised as well. He complimented Sapssky afterward. Said something like "when Spassky applauded me, I realized he was a classy opponent" Something like that.

The scene of Spassky in his room talking to the "listening device" sums up the Russian point of view. Spassky wasn't a party line type. Geller was, which is why he was assigned to keep Spassky straight (and from defecting), and why Spassky assumed that Geller was listening to him along with Brezhnev.

It's a good question. One would think that scene was constructed for dramatic effect. But there's nothing more dramatic than real life. It must've been something to witness that moment when the reigning Soviet world champion stood up and applauded his American challenger in the middle of the Cold War. This was a testament to Spassky's class and Fischer's genius. Understand this: Spassky was an awesome chess player. One does not become chess world champion by accident. He appreciated Fischer's artistry to THAT degree.

It did not happen in the exaggerated way shown in the film. What really happened was that when Spassky resigned the game, the audience and crowd applauded loudly and then Spassky also joined in. It was nevertheless still a fine show of sportsmanship on Spassky's part.