How long does it take a letter to reach London? -- [teacher's version]
How long does this letter take to arrive at London? -- [classmate's version]
The teacher's version (#2) sounds good. That is, it is acceptable and is standard English.
Your classmate's version (#3) sounds unusual, and is probably unacceptable. (Though, some of the problem might be due to the subject "this letter".)
Let's look a bit at your teacher's version #2:
- How long does it take a letter to reach London? -- [teacher's version]
But let's insert the word "for" in there to see how it looks:
- A. How long does it take [for a letter to reach London]?
This version #A basically means the same thing as version #2 (the teacher's version).
I'm going to spend a hunk of the analysis on that version #A, because what I want to show will show up cleaner this way, or so I hope.
Let's now look at version #A and some versions that could correspond to it:
B. It takes five days [for a letter to reach London]. -- [sentence is a declarative clause]
C. It takes how long [for a letter to reach London]? -- [interrogative clause, with interrogative phrase in situ]
D/A. How long does it take [for a letter to reach London]? -- [interrogative clause, with interrogative phrase fronted]
Notice that version #D (which is identical to #A) has subject-auxiliary inversion, which was done due to the fronting of a non-subject interrogative phrase ("how long").
In version #D, we can see that the pronoun "it" is the subject because it had undergone subject-auxiliary inversion and also because it is sandwiched between the auxiliary verb ("does") and the lexical verb ("take"). That the word "it" is sandwiched like that definitely shows that the word "it" is the grammatical subject of the main clause.
Let's look a bit deeper at version #B. We see that the subject is the dummy pronoun "it", and that the infinitival clause "for a letter to reach London" is sorta like a semantic-subject for the sentence--this is why this pronoun "it" is considered to be a dummy pronoun, because it has no semantic meaning in itself. In other words, version #B has the meaning of the below version #E, but #E is less likely to occur than version #B:
Version #B is called an extraposition construction because there's an extra position in the clause, one that is filled by that extra word "it", when compared to the more basic version #E.
The reason why extraposed version #B is more likely to be used than #E is that #E's subject is a subordinate infinitival clause, which means that the subject is a clause and that means that the subject will usually be relatively heavy in weight when compared to the other elements in a sentence, and there is a strong preference to have heavy stuff moved to the end of the sentence, thus, the extraposed version is often preferred (by the speaker/writer).
Now, having gone through all that, let's go and look at the teacher's version #2:
- How long does it take [a letter] to reach London? -- [teacher's version]
We can see that the word "it" is the grammatical subject of version #2. That's because the word "it" is sandwiched between the auxiliary verb ("does") and the lexical verb ("take").
So, there is a lot of similar stuff between version #2 and the above heavily analyzed version #A. But there is a big difference: in version #2, the so-called semantic-subject is the noun phrase "a letter" (while #A's semantic-subject is the infinitival clause "for a letter to reach London"). We can see this if we replace the dummy pronoun "it" of #2 with that noun phrase "a letter":
- 2.s How long does [a letter] take to reach London?
Also, because version #2s doesn't lose any semantic meaning due to the deletion of the word "it", that indicates that the word "it" is a dummy pronoun (i.e. it has no semantic meaning).
Let's look at some versions that could correspond to version #2s:
2.t [A letter] takes five days to reach London. -- [declarative clause]
2.u [A letter] takes how long to reach London? -- [interrogative clause, with interrogative phrase in situ]
2.v/s How long does [a letter] take to reach London? -- [interrogative clause, with interrogative phrase fronted]
Those above versions (#2s-v) seem to be okay. The difference between them and the previous versions (#A-D) is one that is more of pragmatics--in this case, of information packaging. That is, the subject in #A-D is a dummy pronoun "it", and so, it will be relatively quite easy to use their sentences in many different contexts -- while versions #2s-v have a semantically meaningful noun phrase as their subject and so there will be more restrictions on their sentences as to which contexts they will be acceptable in.
Now let's look at your classmate's version #3:
- How long does [this letter] take [to arrive at London]? -- [classmate's version]
Compared to your teacher's version #2, there are three main differences:
version #3 does not have a dummy pronoun "it" as its subject. Instead, it has a semantically meaningful noun phrase "this letter" as its subject, which means that the contexts that its sentence will be acceptable in are restricted.
version #3 uses a different noun phrase as its meaningful semantic-subject: #3's "this letter" (a definite noun phrase) vs #2's "a letter" (an indefinite noun phrase).
version #3 uses a different verb ("arrive") in its infinitival clause; and also the infinitival clause uses a preposition phrase ("at London") as a complement instead of a noun phrase ("London") as done in version #2.
Your classmate's version #3 is awkward and probably unacceptable. As to why this is so, it might help if we fiddle around with permutations of version #3, by switching out the three differences in different combinations to see which differences seem to be important.
For instance, if we switch in the verb "reach" (which means we'll also have to exchange out the preposition phrase for the noun phrase "London" to make it grammatical), we'll get:
- 3.a How long does [this letter] take to reach London?
It sounds a little better than before, but it seems to be unacceptable, that is, awkward. The remaining awkwardness might be due to the noun phrase "this letter". (Notice that the awkwardness disappears once we switch in the noun phrase "a letter", but then that version has now become version #2s.)
Let's now try putting that permutation #3a into a construction that uses a dummy pronoun "it" as its subject:
- 3.b How long does it take this letter to reach London?
It sounds a little bit more better, but it is probably still too awkward sounding to be acceptable.
Let's try a permutation where we put your classmate's original version #3 straight into a construction that uses a dummy pronoun "it" as its subject:
- 3.c How long does it take [this letter] to arrive at London?
It too sounds a bit better than your classmate's original version #3.
Let's try permutations of your classmate's version #3 where we switch in the noun phrase "a letter", with and without using a dummy pronoun "it" as subject:
Those changes seem to help a bit, but both of them still seem to be awkward and unacceptable.
So, there seems to perhaps be multiple reasons why your classmate's version #3 ends up being awkward and unacceptable.
One major reason is the difference in type of noun phrase (NP): the definite NP "this letter" used in your classmate's version #3 versus the indefinite NP "a letter" as used in the teacher's version #2.
Another major reason is the difference in the verb in the infinitival clause: the verb "arrive" in your classmate's version #3 versus the verb "reach" in the teacher's version #2.
Interestingly, notice how the acceptability of your classmate's version #3 seems to be improved if we insert the verb "will":
Those versions sound better, but they are probably not yet (fully) acceptable.
Let's insert a "for" into version #3g to turn it into an extraposition construction (#3h), and see how it sounds:
- 3.h How long will it take [for this letter to arrive at London]?
That version #3h sounds better to me, but it is probably still not yet (fully) acceptable.
As to which version would correspond better to the Japanese version #1, that's something that I can't help you with.