In occasione di Natale, compro un regalo per mia madre.

In occasione di is a fixed expression meaning something like on the occasion of, for, or around the time of a special event.

So in occasione di Natale means for Christmas or on the occasion of Christmas.

It is a bit more formal or written-sounding than some other ways to say the same idea.

Yes. A Natale is very common and usually more natural in everyday speech.

So these are both possible:

• A Natale, compro un regalo per mia madre.
• In occasione di Natale, compro un regalo per mia madre.

The difference is mostly tone:

• A Natale = simpler, more everyday
• In occasione di Natale = more formal, more elaborate

Because Natale is being used without an article in this expression.

In Italian, names of holidays often appear without an article, especially in time expressions and fixed phrases:

• a Natale
• per Natale
• in occasione di Natale

You do get an article in other kinds of expressions, for example when Natale is treated more like a regular noun:

• lo spirito del Natale
• la magia del Natale

So in this sentence, di Natale is the normal form.

The comma separates the introductory time phrase from the main clause:

• In occasione di Natale, = introductory phrase
• compro un regalo per mia madre = main statement

In writing, this comma is common and helps readability. It is not always absolutely required, but it is very normal here.

Because the ending of the verb already tells you the subject.

Compro is the first person singular of comprare, so it already means I buy.

Italian often leaves out subject pronouns when they are not needed:

• compro = I buy
• parli = you speak
• andiamo = we go

You would add io only for emphasis, contrast, or clarity:

• Io compro un regalo per mia madre, non per mio padre.

Compro is the present indicative of comprare.

Here it can express a general or habitual action, something like:

• At Christmas, I buy a gift for my mother.

Depending on context, the Italian present can sometimes also sound more immediate than the English simple present, but in this sentence the most natural reading is a general statement or habit.

Un is the masculine singular indefinite article, meaning a or an.

So:

• un regalo = a gift

It is indefinite because the gift is not being identified as a specific, already-known one.

Compare:

• compro un regalo = I buy a gift
• compro il regalo = I buy the gift

In this sentence, per mia madre means for my mother and describes who the gift is intended for.

This is very natural with regalo:

• un regalo per mia madre = a gift for my mother

Italian can also say:

• compro un regalo a mia madre

There, a mia madre works as the indirect object of the verb comprare. Both are possible, but regalo per... is especially common when you are describing the gift itself as being meant for someone.

With singular close family members, Italian usually drops the article before the possessive adjective:

• mia madre
• mio padre
• mio fratello
• mia sorella

So per mia madre is the normal form.

But there are important exceptions. The article often appears:

• with plurals: i miei genitori
• with modified family nouns: la mia cara madre
• in some regional or stylistic usage

So here mia madre is exactly what you would expect.

Yes. Italian word order is fairly flexible.

This sentence can also be phrased as:

• Compro un regalo per mia madre in occasione di Natale.

That version is also correct. The difference is mainly emphasis:

• In occasione di Natale, ... puts the time setting first
• ... in occasione di Natale gives a more neutral flow

Both are natural.

Yes. Regalo is the everyday word for gift or present.

Another word is dono, but that sounds more formal, literary, or ceremonial.

So in a normal sentence like this, regalo is the most natural choice.