В нашей семье принято ужинать вместе.

Here принято means it is customary, it is the done thing, or it is usual.

So В нашей семье принято ужинать вместе means something like:

• In our family, it is customary to have dinner together
• In our family, we usually eat dinner together
• In our family, it’s the norm to have dinner together

A useful thing to know is that принято comes from the verb принять, but in this kind of sentence it works as a fixed impersonal expression meaning it is accepted/customary.

Russian often uses impersonal constructions where English would use it is or a personal subject like we.

So instead of saying something like:

• We in our family customarily eat dinner together

Russian naturally says:

• В нашей семье принято ужинать вместе

Literally, it is closer to:

• In our family, it is customary to dine together

There is no explicit we, because the sentence is talking about a general family custom, not focusing on the people as the grammatical subject.

Because the preposition в here means in, and after в in this meaning, Russian uses the prepositional case.

So:

• семья = family
• в семье = in the family

The adjective наша also has to match the noun, so it changes too:

• наша семья = our family
• в нашей семье = in our family

This is standard adjective-noun agreement:

• feminine
• singular
• prepositional case

Because after принято Russian typically uses an infinitive to say what is customary.

Pattern:

• принято + infinitive

Examples:

• Здесь принято здороваться. = It is customary to say hello here.
• У нас принято снимать обувь. = It is customary at our place to take off your shoes.
• В нашей семье принято ужинать вместе. = In our family, it is customary to have dinner together.

So ужинать is the action that is considered normal or customary.

Because ужинать is imperfective, and that fits the idea of a habit, general practice, or repeated custom.

• ужинать = to have dinner, to eat dinner regularly/in general
• поужинать = to have dinner once, as a completed event

Since the sentence is about what people generally do in the family, the imperfective ужинать is the natural choice.

Compare:

• Мы любим ужинать вместе. = We like having dinner together.
• Сегодня мы поужинаем вместе. = Today we’ll have dinner together.

So принято ужинать вместе sounds natural because it refers to an ongoing custom.

Вместе means together.

In this sentence it modifies ужинать:

• ужинать вместе = to have dinner together

Its position is quite natural at the end, but Russian word order is flexible. You could also hear:

• В нашей семье вместе ужинать принято.

But the original order:

• В нашей семье принято ужинать вместе

is the most neutral and natural.

Not really in the usual sense.

Historically, принято is the short neuter form of a passive participle from принять, but in this sentence it functions more like a predicative word in an impersonal expression.

For a learner, the most useful thing is to treat:

• принято + infinitive

as a set pattern meaning:

• it is customary to ...
• it is normal/accepted to ...

So you do not need to analyze it as a normal adjective modifying a noun.

Yes, absolutely.

• В нашей семье принято ужинать вместе
• У нас в семье принято ужинать вместе

Both are natural and mean roughly the same thing: In our family, it is customary to have dinner together.

The version with у нас can sound a little more conversational.
The version with в нашей семье sounds slightly more explicit or formal.

Usually no. It mainly expresses custom, tradition, or what is normally done, not a strict rule or obligation.

So it suggests:

• This is our family habit
• This is how things are usually done in our family

If you wanted a stronger idea of obligation, Russian would use different wording, for example with words meaning must or need to.

It is completely natural and idiomatic.

It sounds like something a native speaker would say when describing a family tradition or social norm.

The structure в [place/group] принято + infinitive is very common in Russian for talking about customs:

• У нас принято помогать гостям.
• В этой компании не принято спорить с начальником.
• В нашей семье принято ужинать вместе.

So this is a very useful model to learn.