Learn Hardcore Greek: Σκέφτομαι αν θέλω να κάνω μεταπτυχιακό στο εξωτερικό ή στη χώρα μου. - I am thinking about whether I want to do a master’s abroad or in my country.

σκέφτομαι is in the middle/passive form, but its meaning is active: I think / I am thinking.
There is a form σκέφτω, but in contemporary Greek it is rare/archaic and basically not used in everyday speech.

So, you should always say σκέφτομαι when you mean I think / I’m thinking.

What exactly does αν mean here? Is it if or whether?

In this sentence, αν corresponds to English whether:

Σκέφτομαι αν θέλω να κάνω…
→ I’m thinking *whether I want to do…*

Greek αν covers both English if and whether, depending on context:

Αναρωτιέμαι αν θα έρθει. → I wonder *whether he will come.*
Αν βρέχει, δεν θα πάμε. → If it rains, we won’t go.

Here, because you’re considering two options (abroad or in my country), English uses whether, but Greek still just uses αν.

Why do we say θέλω να κάνω and not something like a single future form “θα μεταπτυχιάσω”?

Greek normally expresses want + action with the structure:

θέλω + να + verb (subjunctive)
→ θέλω να κάνω = I want to do

There is no natural single verb like “να μεταπτυχιάσω” meaning to do a postgraduate degree in this sense. Instead, Greek uses:

κάνω μεταπτυχιακό = do a postgraduate degree / do a master’s

So θέλω να κάνω μεταπτυχιακό literally is I want to do a postgraduate degree. A future like θα κάνω μεταπτυχιακό would mean I will do a postgraduate degree (a decision or prediction), not I want to do one.

What is the role of να in θέλω να κάνω?

να is the particle that introduces a subjunctive verb form. After verbs of desire, intention, effort, etc., Greek uses:

θέλω να κάνω (I want to do)
προσπαθώ να κάνω (I try to do)
ελπίζω να κάνω (I hope to do)

So να + κάνω here works like English to do, but grammatically it is the subjunctive, not an infinitive (Greek doesn’t have a true infinitive in modern usage).

Why is there no article before μεταπτυχιακό? Why not να κάνω ένα μεταπτυχιακό?

Both are possible, but the article is often omitted in this kind of expression:

να κάνω μεταπτυχιακό
να κάνω ένα μεταπτυχιακό

Meaning-wise, they’re very close: to do a master’s / a postgraduate degree.

In Greek, with some “activity nouns” after verbs like κάνω, σπουδάζω, παίζω, the article is frequently dropped when speaking in general:

κάνω μεταπτυχιακό – I’m doing a postgraduate degree
κάνω διδακτορικό – I’m doing a PhD
παίζω ποδόσφαιρο – I play football

Adding ένα can sound a bit more like “one specific” master’s, but in everyday speech many speakers don’t feel a big difference here.

What exactly does μεταπτυχιακό mean here? Is it an adjective or a noun?

Literally, μεταπτυχιακό is an adjective meaning postgraduate.
However, in this sentence it is used as a noun in the neuter singular:

(το) μεταπτυχιακό = a postgraduate degree / a master’s program

So:

κάνω μεταπτυχιακό → I am doing a master’s degree

Greek often uses adjectives as nouns when the noun is understood:

το μεταπτυχιακό (πρόγραμμα) → the postgraduate (program)
το λύκειο from λυκειακό σχολείο → high school

Why is it στο εξωτερικό and not just εξωτερικό?

εξωτερικό by itself is the adjective external / exterior.
The fixed expression στο εξωτερικό literally means in the exterior, but idiomatically it means abroad.

στο εξωτερικό = abroad
Πήγα στο εξωτερικό. = I went abroad.

It’s made of:

σε (in/to) + το (the) + εξωτερικό → στο εξωτερικό

So you almost always say στο εξωτερικό for abroad, not just εξωτερικό on its own.

Why do we say στη χώρα μου and not στην χώρα μου?

The full form of the article + preposition would be:

σε
- την χώρα → στην χώρα

However, in modern spoken and written Greek there is a common elision (dropping the final -ν) before certain consonants, including χ. So:

στην χώρα → στη χώρα

Both στην χώρα and στη χώρα are grammatically possible, but στη χώρα μου is more typical and smoother in everyday usage.

What case is χώρα in, and why?

χώρα here is in the accusative singular:

nominative: η χώρα (the country)
accusative: τη(ν) χώρα (the country, as an object)

The preposition σε (in, at, to) takes the accusative:

σε
- τη χώρα μου → στη χώρα μου
  = in my country

So χώρα is accusative because it follows σε.

Could I move words around, for example: Σκέφτομαι να κάνω μεταπτυχιακό στο εξωτερικό ή στη χώρα μου? Is that still correct?

Yes, that word order is also correct:

Σκέφτομαι αν θέλω να κάνω μεταπτυχιακό στο εξωτερικό ή στη χώρα μου.
Σκέφτομαι να κάνω μεταπτυχιακό στο εξωτερικό ή στη χώρα μου.

These two are not just a reordering; they slightly change the meaning:

αν θέλω να κάνω = I’m thinking whether I want to do it.
να κάνω (without αν θέλω) = I’m thinking of doing it.

But in terms of word order flexibility (where to put στο εξωτερικό / στη χώρα μου), Greek allows several natural arrangements, as long as the relationships remain clear. Your version is natural and common.

What is the nuance of Σκέφτομαι αν θέλω να κάνω… compared with Σκέφτομαι να κάνω…?

Σκέφτομαι αν θέλω να κάνω μεταπτυχιακό…
→ You are questioning your desire or decision itself: Do I actually want to do a postgraduate degree or not, and where?
Σκέφτομαι να κάνω μεταπτυχιακό…
→ You are considering the possibility/plan: I’m thinking of doing a postgraduate degree… (the desire is more or less assumed).

So the original sentence emphasizes the internal doubt or decision process about whether you want it, not just the plan.