"When is your business trip?"
Right, but the correct pinyin for "出差" is "chūchāi", regardless of the more common pronunciation of "差". When pronounced "chāi", "差" means "send" or "dispatch".
Collins gives the following example:
校长差他去参加研讨会。 (Xiàozhǎng chāi tā qù cānjiā yántǎohuì.) The principal is sending him to attend the seminar.
No, "time-when" or "point-in-time" phrases typically go at the beginning of the predicate (i.e. after the subject) whether in a statement or a question. (In a statement they can go before the subject in some situations.)
Duration phrases usually go at the end, e.g. "你出差几天？" (These can move in front of the verb if used to mean "in the span of", e.g. "我一个星期出差三次", in which case we could say they act as "time-when" phrases.)