This is one of their practices, to invite you to a dinner or a function where a Russian will be present, present because they themselves invited them, and then use that as “evidence” to surveil you.
They also did it to Flynn.
As for Page, I’m not 100% sure he wasn’t a witting participant. Based on his past, I would expect he was in on it, though he says he was not.
Yeah, that was the trap. They wanted to make the appearance of Russian collusion, so they trapped these low level campaign people in situations as you described.
As for Page, you could be right. But it’s hard to imagine that he actually agreed to let them wiretap his communications. I think the FBI just turned on him, presenting him to the FISA court as something they knew he was not.