It is not really wrong, however the verb "to trust" is rather "ufać" than "wierzyć". You can believe someone (believe what he says) and you can also trust him - this is something more than just to believe him.

No, that won't make grammatical sense.

It is dative. See the expandable table here: Polish pronouns / Third-person pronouns or here in Polish: Język polski - zaimki / Zaimki rzeczowne

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