The course creators might have meant “believes” in the sense of “accepts as true”, i.e. “he believes that your faith is sincere and not an act”. Your examples show a strong sense that the phrasal verb “believes in” was their intended meaning (which is analogously creid i in Irish).
Yes, that is the sense that I assumed was meant. The interpretation that you suggest, i.e. 'he believes your show of faith' or 'believes your assertion of faith' (believes that it is sincere), did not occur to me - probably because faith on its own is an internal mental state not accessible to someone else's scrutiny or judgement.
I'd accept it in the sense of "He believes that you're faithful," which allows for that scrutiny. But not sure if that's the sense here, given that it's not using a subordinate clause with an adjective.
EDIT: as of this writing, PatHargan, we are both on 87-day streaks. Synchronicity! \^__^/
As I’d mentioned above, a native English speaker might say “He believes your faith” to mean “He accepts that your faith is sincere and not an act” — as a native English speaker, that is what I would mean by “He believes your faith”. I wouldn’t say that to mean “He believes in (i.e. shares) your faith”.
I love how people over interpret things sometimes.
I believe that the only intent here was to use a sentence to différenciate the verb from the noun. And this is probably the main reason behind most broken English used, which might be correct in a very forced way and restricted situation, but was mostly put there either as a pun, or to make a point about words that can be confused in either language. (Remember Hungary is hungry?)