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sakura trusted fai because thats what she would do. she's known fai for over 2 years, so why, once she gained her forsight power, would that change? she knows that fai is a gentle person at heart, that fai's grown to love all of them. and inside subaru's bubble, she saw how fai tried to protect C!Syao.... so despite knowing that fai lied about many things, deep down fai cares for the group. she pities fai's past, not scorns him for his wrong doings.
besides...despite them being wrong, fai;'s intentions were noble. how can you blame someone for loving someone theyve lost?
and your right, once in tokyo, fai started to relize that no matter hoe noble they were, fai's wish was wrong. so he tried to make up for his past deeds, his lies.