"When do they go to school?"
Yes, you can also say 去上学. FYI, 什么时候 can be replaced by 何时 if you want to sound formal (I'm a native speaker).
There are rules, but they are not difficult. Just Duolingo is not delivering them well enough.
Basically the time can be put at 2 places, either at the very beginning of the sentence, or before the verb (and before other adverbial phrases, if any). It is certainly not more difficult than many other languages.