Learn Dutch: De camera moet om kwart voor tien gerepareerd zijn. - The camera must be repaired at a quarter to ten.

This is the core difference between a state and an action. Using moet ... gerepareerd zijn means that by 9:45, the camera must be in the finished state of being fixed. If the sentence used moet ... gerepareerd worden, it would mean the actual action of repairing needs to take place exactly at 9:45.

Could I change the order of the verbs at the end and say zijn gerepareerd?

Yes, in a standard main clause verb cluster like this, you can often swap the auxiliary and the past participle. Both gerepareerd zijn and zijn gerepareerd are grammatically correct at the end of the sentence, though placing the past participle first is generally more common in spoken Dutch.

Why does the sentence use om for the English 'at'? Can I use op?

For specific times on the clock, Dutch always uses the preposition om (like om kwart voor tien). You would use op for days of the week or specific dates (like op maandag).

How would the English translation change if I wanted to make the Dutch distinction clearer?

English often uses 'must be repaired' for both the action and the state. To make the Dutch meaning of moet ... zijn perfectly clear, you could translate it as 'The camera has to have been repaired by a quarter to ten.' This explicitly highlights that the work must already be completely finished by that time.