Η αδερφή μου γιορτάζει τα γενέθλιά της τον Δεκέμβριο, αλλά εγώ προτιμώ τα Χριστούγεννα από την Πρωτοχρονιά.

In Greek, it is very common to use the definite article with family members and many other nouns, even when there is a possessive like μου (my).

So:

• η αδερφή μου = my sister
• literally: the sister my

This is normal Greek structure. English usually does not use the here, but Greek usually does.

Greek possessive weak pronouns usually come after the noun:

• η αδερφή μου = my sister
• τα γενέθλιά της = her birthday
• το βιβλίο μου = my book

This is one of the most basic word-order differences from English. English says my sister; Greek usually says the sister my.

Both exist.

• αδερφή is very common in everyday Modern Greek.
• αδελφή is also correct and may sound a bit more formal or conservative.

So Η αδερφή μου is completely natural and standard.

Yes. γιορτάζω means to celebrate.

So:

• Η αδερφή μου γιορτάζει τα γενέθλιά της
  = My sister celebrates her birthday

In Greek, this verb is very natural with birthdays, name days, holidays, and similar occasions.

The form γιορτάζει is the 3rd person singular present tense:

• I celebrate = γιορτάζω
• she/he celebrates = γιορτάζει

In Greek, birthday is normally expressed with the plural noun γενέθλια.

So Greek says:

• τα γενέθλια = birthday / birthday celebration

Even though English uses the singular birthday, Greek uses a plural form. That is just how the concept is expressed idiomatically.

Examples:

• Σήμερα είναι τα γενέθλιά μου. = Today is my birthday.
• Γιορτάζω τα γενέθλιά μου. = I’m celebrating my birthday.

This is because of the possessive pronoun της (her).

The basic form is:

• τα γενέθλια = the birthday

But when a weak possessive pronoun follows, Greek often changes the stress:

• τα γενέθλιά της = her birthday

This stress shift is very common in words of this type. You will also see:

• τα πράγματά μου = my things
• τα παιδιά της = her children
  (not every noun changes in exactly the same way, but stress changes before weak pronouns are a common pattern)

So γενέθλιά της is the normal form here.

Because Greek usually uses the weak possessive pronoun after the noun:

• μου = my
• σου = your
• του = his / its
• της = her
• μας = our
• σας = your
• τους = their

So:

• τα γενέθλιά της = her birthday

The form αυτής is not the normal possessive form here. It is a stronger pronoun used in other contexts, not the usual way to say her after a noun.

Greek very often uses the definite article with months.

So:

• τον Δεκέμβριο = in December

This is especially common when expressing time. The article shows the accusative case used adverbially for time expressions.

Other examples:

• τον Ιανουάριο = in January
• τον Μάιο = in May
• τον Αύγουστο = in August

English does not use the here, but Greek usually does.

Yes. Δεκέμβριος is the dictionary form, which is the nominative.

Here, after τον, it becomes the accusative:

• ο Δεκέμβριος = December
• τον Δεκέμβριο = in December

This is a normal masculine noun pattern:

• ο φίλος → τον φίλο
• ο χρόνος → τον χρόνο
• ο Δεκέμβριος → τον Δεκέμβριο

Yes, Greek could absolutely say just αλλά προτιμώ.

Greek often drops subject pronouns because the verb ending already shows the subject:

• προτιμώ = I prefer

But εγώ is added here for contrast:

• My sister celebrates her birthday in December, but I prefer Christmas to New Year’s.

So εγώ adds emphasis, something like:

• but as for me
• but I personally

Yes. With προτιμώ, Greek commonly uses από to show what something is preferred over.

So:

• προτιμώ τα Χριστούγεννα από την Πρωτοχρονιά = I prefer Christmas to New Year’s = literally I prefer Christmas from/over New Year’s

This is a standard Greek pattern.

You may also encounter other ways of expressing comparison in Greek, but προτιμώ X από Y is very common and natural.

Because in Greek, holiday names often appear with the definite article.

So:

• τα Χριστούγεννα = Christmas
• την Πρωτοχρονιά = New Year’s / New Year’s Day

Again, this is more article-heavy than English. Greek often says:

• Τα Χριστούγεννα έρχονται σύντομα. = Christmas is coming soon.
• Την Πρωτοχρονιά θα μείνουμε σπίτι. = On New Year’s Day we’ll stay home.

Because Χριστούγεννα is a plural neuter noun in Greek.

So Greek treats Christmas as grammatically plural:

• τα Χριστούγεννα

This is just the standard word. You do not normally try to make it singular in everyday use.

Greek has several holiday expressions like this where the grammar does not match English one-to-one.

Πρωτοχρονιά usually means New Year’s Day or the New Year holiday/occasion.

It does not normally mean New Year’s Eve.
For New Year’s Eve, Greek usually says:

• Παραμονή Πρωτοχρονιάς = New Year’s Eve

So in this sentence:

• προτιμώ τα Χριστούγεννα από την Πρωτοχρονιά most naturally means
• I prefer Christmas to New Year’s / New Year’s Day

Because it is the object of από in this comparison structure, so it appears in the accusative with the article:

• η Πρωτοχρονιά = New Year’s Day
• την Πρωτοχρονιά = accusative form

This is a regular feminine noun pattern:

• η γιορτή → τη(ν) γιορτή
• η χαρά → τη(ν) χαρά
• η Πρωτοχρονιά → τη(ν) Πρωτοχρονιά

The full phrase is:

• από την Πρωτοχρονιά

It can definitely be habitual.

Greek present tense often covers both:

• something happening now
• something that happens generally / habitually

So:

• Η αδερφή μου γιορτάζει τα γενέθλιά της τον Δεκέμβριο does not mean she is celebrating right now at this exact moment. It can simply mean:
• My sister celebrates her birthday in December
• My sister’s birthday is in December and she celebrates it then

This is very similar to English simple present.

Yes, to some extent. Greek word order is more flexible than English, though not completely free.

For example, the original sentence is very natural:

• Η αδερφή μου γιορτάζει τα γενέθλιά της τον Δεκέμβριο, αλλά εγώ προτιμώ τα Χριστούγεννα από την Πρωτοχρονιά.

But Greek can move parts around for emphasis. For example:

• Τον Δεκέμβριο η αδερφή μου γιορτάζει τα γενέθλιά της... puts more focus on in December.

Still, for learners, the original order is a very good neutral model.

Then Greek would very naturally drop εγώ:

• Η αδερφή μου γιορτάζει τα γενέθλιά της τον Δεκέμβριο, αλλά προτιμώ τα Χριστούγεννα από την Πρωτοχρονιά.

This means the same basic thing, but with less contrastive emphasis on the speaker. The version with εγώ sounds a bit more pointed:

• but I prefer...