The boy stole / was stealing the apples while nobody was looking / looked.
Question: Which variant is more appropriate?
The second verb, to look should be in past progressive. It's about an action that was (or in this case was not) going on during another action.
The first could go either way, depending on context. Is there some other activity going to be mentioned that is also located in time during the apple theft? For example, if the next sentence were to start:
It suddenly occurred to him that stealing was naughty
Then the progressive is most appropriate for to steal as well. The same is true if the sentence were in answer to the question "what was the boy doing at 2pm yesterday?", but that would be an unusual case.
If nothing like that applies, then stole is more natural. Past progressives are usually used when locating actions in time, either to specific times or in relation to other actions. However, I can't say that using the progressive in this case would be wrong as such, just strange.