Porodica je zajedno za Božić.

• Porodica = family
• je = is
• zajedno = together
• za = for / at / during (depending on context)
• Božić = Christmas

So grammatically it is:

• Porodica — subject
• je — the verb to be
• zajedno — an adverb describing the situation
• za Božić — a time expression meaning for/at Christmas

Je is the 3rd person singular present form of biti (to be).

Because porodica is singular, Serbian uses singular je:

• Porodica je zajedno. = The family is together.

In standard Serbian, you normally do not omit this verb in a sentence like this. So:

• Porodica je zajedno = correct
• Porodica zajedno = not a normal full sentence in standard speech, except maybe in headlines or very stylized language

Because porodica is grammatically a singular noun, even though it refers to a group.

This is similar to English family when you say:

• The family is together.

In Serbian, the verb agrees with the noun porodica, not with the number of people inside the family. So:

• Porodica je... = singular

Serbian does not have articles like English a and the.

So porodica can mean different things depending on context:

• a family
• the family
• sometimes just family in a general sense

In this sentence, English would most naturally translate it as the family or possibly the family is together at Christmas.

If Serbian speakers want to be more specific, they usually do it through context or with extra words, for example:

• moja porodica = my family
• ta porodica = that family

Zajedno is an adverb, and it means together.

It does not change for gender, number, or case. Its form stays the same.

Compare:

• Mi smo zajedno. = We are together.
• Porodica je zajedno. = The family is together.

It describes the state of being united or in one place.

Here za Božić means something like:

• for Christmas
• at Christmas
• during Christmas time

With holidays, Serbian often uses za to place something in the context of that holiday.

Examples:

• Dolazimo za Božić. = We’re coming for Christmas.
• Porodica je zajedno za Božić. = The family is together for/at Christmas.

So za Božić is functioning as a time expression.

After za in this kind of expression, Serbian uses the accusative.

So grammatically this is:

• za + accusative

Here the noun is Božić. Because Božić is a masculine inanimate noun, its nominative and accusative singular look the same:

• nominative: Božić
• accusative: Božić

So the form does not visibly change, but the case is still accusative because of za.

This is a very common question.

A useful basic distinction is:

• za Božić = for Christmas / at Christmas / during the Christmas period
• na Božić = on Christmas Day

So:

• Porodica je zajedno za Božić. suggests the family is together for the holiday
• Vidimo se na Božić. often means See you on Christmas Day

In real life, usage can overlap a bit depending on speaker and region, but this distinction is a good one for learners.

Yes. Serbian word order is more flexible than English word order.

The sentence as given is natural and neutral:

• Porodica je zajedno za Božić.

But you can move things around to change emphasis:

• Za Božić je porodica zajedno. — emphasizes at Christmas
• Zajedno je porodica za Božić. — possible, but less neutral and more marked

So the original version is a good standard choice.

Yes, it is natural and understandable.

It clearly means that the family is together at Christmas time.

A speaker might also say something a bit more idiomatic depending on the exact meaning, for example:

• Porodica je na okupu za Božić. = The family is all together for Christmas.

But Porodica je zajedno za Božić. is perfectly good Serbian.

A few important sounds:

• j is pronounced like English y in yes
• ž sounds like the s in measure
• ć is a soft ch-like sound, softer than English ch

So:

• Božić sounds approximately like BO-zheech, but with a softer final sound than regular English ch
• zajedno is roughly za-YED-no
• je is roughly ye

A rough pronunciation of the whole sentence is:

• po-RO-di-tsa ye za-YED-no za BO-zheech

Not exact IPA, but close enough to help an English speaker get started.