Could you tell me whether this sentence is an inverted sentence?

Question

I read a conversation in a IELTS listening test

Oh, I see, and how long can I hang on to them for?

so, normally, it should be

oh, I see, and how long can I hang on to for them?

Am I right?

Answer 1

This is not a matter of inversion but of what linguists call "pied-piping" vs "stranding".

That is, the canonical declarative form which underlies your question is

                 I can hang on to them for [TIME EXPRESSION].

Note that TIME EXPRESSION is the complement of the preposition for. For is not related to them.

When you turn this into a question, you substitute the interrogative phrase how long for [TIME EXPRESSION] and move how and its complement to the front of the sentence, and you invert the subject I and the auxiliary can:

                I can hang on to them for [TIME EXPRESSION]. 
                 ⇘⇙                              ⇓
           ⇐  ⇐  ⇐  ⇐  ⇐  ⇐  ⇐  ⇐  ⇐  ⇐  how long
         ⇓       ⇙⇘
       How long can I hang on to them for?

Note that How long is now separated from the preposition which governs it, for; for is said to be "stranded". In formal writing it helps make the relationship clearer if you "pied-pipe" the preposition along with the interrogative, like this:

                I can hang on to them for [TIME EXPRESSION]. 
                 ⇘⇙                   ⇓          ⇓
           ⇐  ⇐  ⇐  ⇐  ⇐  ⇐  ⇐  ⇐for      how long
         ⇓       ⇙⇘
   For how long can I hang on to them?

So either of these constructions is correct:

How long can I hang on to them for? ... is probably most common in speech
For how long can I hang on to them? ... is preferred in the most formal writing.