adding some thoughts here as a native speaker:
You can say 前几天爸妈去出差了。There's no semantic difference to me in this case.
Under the hood, the syntax are different. In 去出差, 去 indeed means "to go", and ...
买 is a transitive verb; 买东西 is a separable Verb-Object structure, so the number + measure goes between.
to eat/ to have eaten a meal
to sing/ to have sung two songs
Now that you only question about grammar, let's just talk about grammar. I found a well written elucidation, though, and paste the link here for reference.
1.無 serves as a ...
上网 is a Verb Object construction internally ("ascend net" = to get on the web). 上网购物 is a Serial Verb construction: first action 上网, second action 购物. Both actions are equal, not subordinate/main, as ...
Horizontal to vertical is pretty simple in modern Chinese. Vertical Chinese is read from the top down - so the first one goes at the top and then the rest follow one by one.
多为和平 would be written:
Tl;dr: There is inherent adverbial order in Chinese (point 2.). Sentences with the same adverbs ordered differently can have different meanings (points 3. to 6.).
The correct order is 你平時/一般什麼時候做作業？.
1-这个故事发生在上个世纪末. I wonder if 发生 could be placed after 在上个世纪末. Shouldn't time be placed before a verb?
昨天，明天，一小時前，or 十分鐘後 are 'time particles' that indicate when the verb occurs.
在昨天，在明天，在一小時前，or 在十分鐘後 ...
Well, you have received several answers from native speakers. But I'd like to add some contexts and hope that would help you understand it better.
It is acceptable and understandable. 作業他一點都沒做。(He did not even do small amount of homework.)
Think the component as [thing][person][description used to denote less amount of thing][description used ...