Q: "Did I charter a train and take it to the sea?" vs. A: "I did charter a train and took it to the sea." How to explain to a learner the usage diff.?

The trick is to pick the right bracketing.

Consider the following pair:

• I (did charter a train) and (took it with me).
• I did (charter a train and take it with me).

In the first case, the did phrase terminates before took, so we can expand the sentence to "I did charter ... and I took ...".

In the second case, did applies to both verbs, so the expansion is "I did charter .. and I did take".

If you remove the brackets from the bulleted pair, you end up with the odd situation where a simplistic scanning seems to suggest that "took" and "take" both convey the same sense. The parsing explains the oddity.

"Yes, I did charter a train and took it to the sea."

I agree with Lawrence. I would add that to use the above sentence correctly, one should repeat "I"

"Yes, I did charter a train and I took it to the sea."

The reason is that mentally we try to make "I" cover both verbs but then discover that they are incompatible. By repeating "I", we make it clear that the first "I" does not apply to the second verb.

You are mixing up a few concepts here.

“Did I charter?” has auxiliary “to do” with subject-verb inversion. This is not the past perfect because perfects are formed with auxiliary “to have”.

When you use auxiliary verbs, the first one is inflected for tense and person, while the lexical verb (here, “to charter” and maybe “to take”) must be in the base, -ed or -ing form.

Subject-verb inversion is used for most (but not all) questions. However, inverting most verbs is now seen as archaic (“Chartered I?”), so we add the auxiliary “to do” and invert that instead. When you’re not inverting, “to do” isn’t needed, so doing it anyway adds emphasis, called “emphatic do”, as in “I did charter”.

Now to the parallelism aspect. Both versions “I did charter and (I did) take” and “I did charter and (I) took” are grammatical, but by putting back in the elided words, we can see the “to take” half is emphatic in the first case and not in the second. Which is correct depends on what you mean to say.