Νομίζω ότι η φίλη σου έχει δίκιο για το καινούριο διαμέρισμα.

Ότι means that and introduces a subordinate clause after Νομίζω (I think).

So:

• Νομίζω = I think
• ότι η φίλη σου έχει δίκιο... = that your friend is right...

In English, that is often optional: I think (that) your friend is right.
In Greek, ότι is very commonly used, though in everyday speech people also often use πως in the same kind of sentence:

• Νομίζω ότι...
• Νομίζω πως...

Both are normal here.

Η is the feminine singular definite article, meaning the.

• η φίλη = the friend / the female friend
• σου = your

So η φίλη σου literally means the friend of yours, but naturally it means your friend.

Greek very often uses the definite article where English does not. With possessives, this is especially common:

• ο αδερφός μου = my brother
• η μητέρα σου = your mother
• το σπίτι τους = their house

So the article is not extra or unusual here; it is the normal Greek pattern.

Yes. Η φίλη is feminine, so it refers to a female friend.

Compare:

• ο φίλος = male friend
• η φίλη = female friend

In English, friend does not usually show gender, but Greek nouns normally do. So the sentence clearly tells you that the friend is female.

In Greek, weak possessive forms like μου, σου, του, της, μας, σας, τους usually come after the noun.

So:

• η φίλη σου = your friend
• το σπίτι μου = my house
• ο δάσκαλός της = her teacher

This is one of the basic differences from English. English says your friend, but Greek usually says something more like the friend your in word order.

Έχει δίκιο is a very common Greek expression meaning is right.

Literally, it is:

• έχει = has
• δίκιο = right / justice / justification

So literally it is something like has right or has justification, but idiomatically it means:

• be right
• be correct

Examples:

• Έχεις δίκιο. = You’re right.
• Δεν έχεις δίκιο. = You’re not right.
• Η φίλη σου έχει δίκιο. = Your friend is right.

This is just the normal Greek way to express the idea.

Because Greek uses the expression έχω δίκιο for to be right.

So although English uses the verb to be, Greek uses to have:

• είμαι κουρασμένος = I am tired
• είμαι έτοιμος = I am ready
• but έχω δίκιο = I am right

This is something you simply learn as a fixed expression.

Δίκιο is in the accusative singular, because it is the direct object of έχει.

• έχει = has
• what does she have? δίκιο

So grammatically it behaves like an object:

• Έχω χρόνο. = I have time.
• Έχω χρήματα. = I have money.
• Έχω δίκιο. = I am right.

The form δίκιο is the normal neuter singular accusative/nominative form of this word in this expression.

Για usually means for or about, and here it means about / concerning.

So:

• για = about
• το καινούριο διαμέρισμα = the new apartment

Together:

• για το καινούριο διαμέρισμα = about the new apartment

This phrase tells you what your friend is right about.

Because διαμέρισμα is a neuter singular noun, and the article and adjective must agree with it.

Breakdown:

• το = neuter singular the
• καινούριο = neuter singular new
• διαμέρισμα = neuter singular apartment

Greek adjectives agree with the noun in:

• gender
• number
• case

So if the noun changes, the adjective and article usually change too.

Compare:

• ο καινούριος υπολογιστής = the new computer (masculine)
• η καινούρια τσάντα = the new bag (feminine)
• το καινούριο διαμέρισμα = the new apartment (neuter)

Yes. Both καινούριο and καινούργιο are common forms meaning new.

So you may see:

• το καινούριο διαμέρισμα
• το καινούργιο διαμέρισμα

Both are natural. The version in your sentence, καινούριο, is completely standard.

Also note that Greek has another common word for new:

• νέος / νέα / νέο

But καινούριος often emphasizes new in the sense of brand-new or recently acquired, depending on context.

The sentence is:

• Νομίζω ότι η φίλη σου έχει δίκιο για το καινούριο διαμέρισμα.

A natural breakdown is:

1. Νομίζω = I think
2. ότι = that
3. η φίλη σου = your friend
4. έχει δίκιο = is right
5. για το καινούριο διαμέρισμα = about the new apartment

Greek word order is often more flexible than English, but this version is very neutral and natural.

You could move things around for emphasis, but not all changes are equally natural in every context. For a learner, the sentence as given is an excellent standard model.

Because Greek verbs usually already show the subject through their endings.

• Νομίζω = I think

The ending -ω tells you it is I in the present tense.

So Greek often omits the subject pronoun when it is already clear:

• Νομίζω = I think
• Ξέρεις = you know
• Έχει = he/she/it has

You can add the pronoun for emphasis:

• Εγώ νομίζω... = I think... / As for me, I think...

But without emphasis, leaving it out is more normal.

Yes, για is followed by the accusative.

Here:

• το διαμέρισμα is accusative singular neuter
• the article το and adjective καινούριο match that noun

With many neuter nouns, the nominative and accusative look the same, so you do not see a visible change. But the rule is still that για takes the accusative.

Examples:

• για τον φίλο μου = about my friend / for my friend
• για τη δουλειά = about the job
• για το σπίτι = about the house

Possibly, depending on context, but not necessarily.

• η φίλη σου can mean your female friend
• in some contexts it can also mean your girlfriend

Greek, like English, sometimes relies on context for this. If the speaker wanted to be very explicit, they might choose wording that makes the romantic meaning clearer. But by itself, η φίλη σου does not automatically force the meaning girlfriend.