Reported/Indirect Speech and Past Simple with when. Can they get confused with each other?

Going straight to the point, let's say that I have a sentence like

He asked when the train arrived.

How can I tell whether this is a Past Simple (As soon as the train arrived he asked) or Reported Speech (He: "When does the train arrive?"). Is there a way to distinguish between them? Or maybe I'm doing some other mistake that I'm not aware of?

No. Without context, these are equally possible interpretations: you have a structural ambiguity.

In context, it will usually be clear, because ask is normally transitive, and only if the object (the question or request) is already in the discourse will it be used intransitively. So in

He asked me if I had seen her. He asked when the train arrived.

when the train arrived is an adverbial phrase, but in

He asked when the train arrived.

without context, it is an indirect question.

There is another point though: though the past simple is grammatical here, I think it is likely only because he is talking about something timetabled, like a train. So if he asked

When does the train arrive?

meaning "What time is the train scheduled to arrive?" then you might say

He asked when the train arrived.

But if he asked about an individual particular event, such as:

When do you go?

then to my ears

He asked when I went.

is unclear, and I'd be much more likely to say

He asked when I was going.