Δεν ξέρω σε ποιο βαγόνι είναι η φίλη μου.

Because ξέρω and είναι are in the indicative, and the normal negation for the indicative in Modern Greek is δεν.

Use μη(ν) mainly with:

• the subjunctive
• commands / prohibitions
• certain fixed expressions

For example:

• Δεν ξέρω = I don’t know
• Μην πας = Don’t go

So Δεν ξέρω... is exactly what you expect here.

Because Greek uses σε to express location very often.

Here, σε ποιο βαγόνι means in which carriage / car.

In Modern Greek, σε + accusative can cover meanings that English expresses with different prepositions, such as:

• in
• at
• to

So even though English says in which car, Greek says σε ποιο βαγόνι.

It is accusative singular neuter, because it follows σε, and σε takes the accusative in Modern Greek.

Also:

• βαγόνι is a neuter noun
• ποιο agrees with βαγόνι in gender, number, and case

A useful detail: for many neuter nouns and adjectives, the nominative and accusative forms are identical, so the form ποιο βαγόνι looks the same in both cases.

Because ποιο has to agree with βαγόνι, which is neuter singular.

The forms of ποιος are:

• ποιος = masculine
• ποια = feminine
• ποιο = neuter

Since βαγόνι is neuter, the correct form is ποιο.

Because ποιο is already determining the noun.

In English, which car also has no article, and Greek works similarly here:

• σε ποιο βαγόνι = in which car

You would not normally say σε το ποιο βαγόνι in this kind of sentence.

Because Greek normally uses the definite article with possessive expressions.

So Greek says:

• η φίλη μου = my friend
• το σπίτι μου = my house
• ο αδερφός μου = my brother

To an English speaker, this can look like the my friend, but that is just the normal Greek pattern.

Because the weak possessive pronouns in Greek usually come after the noun.

So:

• η φίλη μου
• το βιβλίο σου
• ο πατέρας της

This is the standard placement. English uses my friend, but Greek uses the equivalent of the friend my.

Greek word order is more flexible than English word order.

After the phrase σε ποιο βαγόνι, it is very natural to put the verb first:

• σε ποιο βαγόνι είναι η φίλη μου

This sounds neutral and normal.

You may sometimes see a different order in Greek, but that usually changes the emphasis or sounds less neutral in this context.

Yes, but είναι is completely natural here.

Greek often uses είμαι for location, just like English uses to be:

• Η Μαρία είναι στο σπίτι. = Maria is at home.

You could also say:

• Δεν ξέρω σε ποιο βαγόνι βρίσκεται η φίλη μου.

βρίσκεται also means is located / is, but it sounds a bit more formal or explicit. In everyday speech, είναι is very common.

Because this is an indirect question.

Greek can say:

• Δεν ξέρω πού είναι...
• Δεν ξέρω πότε έρχεται...
• Δεν ξέρω σε ποιο βαγόνι είναι...

So after ξέρω, you can go straight into the embedded question.

Why not the others?

• ότι means that, and would introduce a statement, not a question
• να is used for the subjunctive, which is not what is happening here

Because the whole sentence is a statement, not a direct question.

The speaker is saying:

• I don’t know...

Inside that statement, there is an embedded question:

• σε ποιο βαγόνι είναι η φίλη μου

So the whole sentence takes a full stop.

Compare:

• Δεν ξέρω σε ποιο βαγόνι είναι η φίλη μου. = statement
• Σε ποιο βαγόνι είναι η φίλη μου; = direct question

Yes, it can, depending on context.

In real Greek, η φίλη μου may mean:

• my female friend
• my girlfriend

Usually the situation makes it clear. If the meaning shown to the learner is my friend, then that is how you should understand it here, but it is good to know that the phrase can be ambiguous in other contexts.