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Eh, what in particular are you talking about?
Angra knows because she is connected to Satoshi and Satoshi has been to the moon cell. She knows because he does.
She explains that in character. The counter force didn't make Archer attack her, thus the logical assumption is that something prevents that, as such she considered the options and came to the conclusion.
Yeah, I'm not convinced about that bit either. Archer is not a Counter Guardian when summoned as a servant, he can act completely freely.
Well aware. That's the reason he could try his plan of escape in fsn. In any case she believes what she said.