Στα Χριστούγεννα η γιαγιά μου φτιάχνει πολλά γλυκά, αλλά την Πρωτοχρονιά τρώμε πιο απλά.

Because στα is the normal contraction of σε + τα.

• σε = at / on / during
• τα = the for a neuter plural noun
• σε τα → στα

So Στα Χριστούγεννα literally looks like at the Christmas holidays, but in natural English it is usually just at Christmas or during Christmas.

In Greek, Χριστούγεννα is a plural-only noun. Greek treats Christmas as a plural holiday word, much like a holiday period.

That is why it takes:

• the plural article τα
• and in this sentence the contracted form στα

So even though English says Christmas as a singular word, Greek says τα Χριστούγεννα.

These are two different time expressions.

• Στα Χριστούγεννα = at / during Christmas
• την Πρωτοχρονιά = on New Year’s Day / at New Year

Πρωτοχρονιά is a singular feminine noun, so you see την, the feminine singular accusative article.

Greek often uses:

• a preposition with some holiday expressions, as in στα Χριστούγεννα
• the accusative by itself for time expressions, as in την Πρωτοχρονιά

Both are completely normal.

In standard Greek, the usual order is:

• article + noun + possessive clitic

So:

• η γιαγιά μου = my grandmother

The little word μου means my, but unlike English, it usually comes after the noun.

Greek normally keeps the article too, so η γιαγιά μου is the most natural form.

Here φτιάχνει means makes or prepares.

With food, φτιάχνω is very common and can mean:

• make
• prepare
• sometimes roughly cook

So η γιαγιά μου φτιάχνει πολλά γλυκά means that the grandmother makes/prepares lots of sweets or desserts.

Because γλυκά is a neuter plural noun here, meaning sweets / desserts.

So the adjective/quantifier must match it:

• πολλά = many / a lot of, neuter plural
• γλυκά = sweets / desserts, neuter plural

They agree in gender, number, and case.

A useful point: γλυκό can mean:

• sweet as an adjective
• dessert / sweet as a noun

Here it is a noun.

Because Greek often leaves out subject pronouns when they are not needed.

The verb ending already shows the subject:

• τρώμε = we eat

So adding εμείς would only be necessary for emphasis or contrast.

Greek does this very often:

• τρώω = I eat
• τρώς = you eat
• τρώμε = we eat

So no separate we is required.

It means more simply or more plainly.

• πιο = more
• απλά = simply / plain(ly)

In this sentence, it means that on New Year’s Day we eat in a simpler way, probably with less elaborate food than at Christmas.

So the contrast is:

• at Christmas: lots of sweets
• at New Year: simpler food or simpler eating

Here it is best understood as an adverb, modifying τρώμε:

• τρώμε πιο απλά = we eat more simply

That said, learners may notice that απλά also looks like the neuter plural form of the adjective απλός. Greek sometimes allows this kind of overlap in form.

In this sentence, the adverb reading is the most natural one.

Because αλλά means but, and Greek normally uses a comma before it when it joins two clauses.

So the structure is:

• Στα Χριστούγεννα η γιαγιά μου φτιάχνει πολλά γλυκά,
• αλλά την Πρωτοχρονιά τρώμε πιο απλά.

This is very similar to English punctuation with but.

Because they are holiday names.

In Greek, names of major holidays are commonly capitalized, especially in standard written language:

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

So the capitalization here is normal.

Yes, but it would sound more emphatic.

• τρώμε πιο απλά = neutral, natural
• εμείς τρώμε πιο απλά = we eat more simply, with extra emphasis or contrast

Since the subject is already clear from the verb ending, Greek usually prefers the shorter version unless there is a reason to stress the subject.