Μου αρέσει το τσουρέκι, αλλά όταν είμαι πολύ νηστικός προτιμώ μπουγάτσα.

Because αρέσει works more like is pleasing to than like the English verb like.

So:

• Μου = to me
• αρέσει = it pleases / is pleasing

So Μου αρέσει το τσουρέκι literally means The tsoureki is pleasing to me.

This is a very common Greek structure. The person who likes something is usually shown with a weak pronoun such as:

• μου = to me
• σου = to you
• του / της = to him / her

Examples:

• Μου αρέσει ο καφές. = I like coffee.
• Σου αρέσει η μουσική; = Do you like music?

The verb agrees with the thing that is liked.

In this sentence, the subject is το τσουρέκι, which is singular, so Greek uses singular αρέσει.

• Μου αρέσει το τσουρέκι. = I like tsoureki.
• Μου αρέσουν τα γλυκά. = I like sweets.

So:

• singular thing liked → αρέσει
• plural things liked → αρέσουν

Μου is a weak personal pronoun, and grammatically it is the genitive form used for meanings like to me or my, depending on context.

Here it means to me:

• Μου αρέσει... = It pleases me / I like...

This is very common in Greek. The genitive weak pronouns often cover functions that English expresses with to:

• μου = to me
• σου = to you
• του / της = to him / her
• μας = to us
• σας = to you (plural/formal)
• τους = to them

Both are possible in Greek, but the article is not always used in exactly the same way as in English.

In Μου αρέσει το τσουρέκι, the speaker is talking about tsoureki as a kind of food in a general sense, and Greek often uses the definite article for that.

In προτιμώ μπουγάτσα, the noun appears without an article, which can sound natural when talking about what one prefers to eat in a general or indefinite way.

So these are both natural:

• Μου αρέσει το τσουρέκι.
• Προτιμώ μπουγάτσα.

You could also hear:

• Προτιμώ τη μπουγάτσα.

That can sound a little more definite or generic depending on context. Greek article usage is flexible and must often be learned through exposure.

Because πολύ here is an adverb, not an adjective.

It modifies νηστικός in the sense of very hungry, so it stays in the adverb form:

• πολύ νηστικός = very hungry

Compare:

• πολύ ψωμί = a lot of bread / much bread
  Here πολύ is adjective-like and relates to a noun.
• πολύ καλός = very good
• πολύ νηστικός = very hungry
  Here πολύ is an adverb meaning very.

So in this sentence, πολύ means very, not many/much.

Yes. Νηστικός is an adjective, so it agrees with the person speaking in gender and number.

Here, είμαι πολύ νηστικός suggests the speaker is masculine singular.

Other possibilities:

• είμαι πολύ νηστική = I am very hungry.
  said by a woman
• είμαστε πολύ νηστικοί = we are very hungry.
  masculine or mixed group
• είμαστε πολύ νηστικές = we are very hungry.
  all-female group

So the ending changes according to who the subject is.

No—this is normal Greek.

Όταν means when, and in a sentence like this it introduces a repeated or general situation:

• όταν είμαι πολύ νηστικός = when I am very hungry

Greek often uses the present tense here just as English does in general statements:

• When I’m very hungry, I prefer...

So the sentence means something habitual or typical, not one specific future event.

Because Greek usually does not need the subject pronoun when the verb ending already shows the subject.

• είμαι = I am
• προτιμώ = I prefer

So εγώ is unnecessary unless you want emphasis or contrast.

For example:

• Προτιμώ μπουγάτσα. = I prefer bougatsa.
• Εγώ προτιμώ μπουγάτσα. = I prefer bougatsa.
  This sounds more emphatic, like contrasting with someone else.

Greek is a pro-drop language, so leaving out subject pronouns is very normal.

Αλλά means but.

It connects the two ideas:

• Μου αρέσει το τσουρέκι = I like tsoureki
• αλλά = but
• όταν είμαι πολύ νηστικός προτιμώ μπουγάτσα = when I’m very hungry, I prefer bougatsa

Its position is straightforward: it comes between the two clauses, just like but in English.

Yes, Greek word order is fairly flexible, although some versions sound more neutral than others.

The original sentence is natural and neutral:

• Μου αρέσει το τσουρέκι, αλλά όταν είμαι πολύ νηστικός προτιμώ μπουγάτσα.

You could also say:

• Μου αρέσει το τσουρέκι, αλλά προτιμώ μπουγάτσα όταν είμαι πολύ νηστικός.

This is also understandable, though the original version may sound a bit smoother because όταν είμαι πολύ νηστικός sets up the condition before προτιμώ.

Greek often moves elements around for emphasis, rhythm, or focus.

Yes, it matters because Greek nouns have grammatical gender.

• το τσουρέκι is neuter
• η μπουγάτσα is feminine

That affects:

• the article: το, η
• adjective agreement, if there is an adjective
• sometimes pronoun reference later in discourse

Examples:

• Το τσουρέκι είναι φρέσκο. = The tsoureki is fresh.
  (φρέσκο matches a neuter noun)
• Η μπουγάτσα είναι ζεστή. = The bougatsa is warm.
  (ζεστή matches a feminine noun)

So even if English does not mark gender on these food words, Greek does.