На семейных праздниках все сначала здороваются, потом обнимаются и только потом садятся за стол.

Because на is being used in the sense of at / during, so Russian normally uses the prepositional case after it.

• праздники = holidays / celebrations
• на праздниках = at celebrations / during celebrations

Here it is also plural, because the sentence is talking about family celebrations in general, not one specific event.

So:

• на семейном празднике = at a family celebration
• на семейных праздниках = at family celebrations

Because семейных is an adjective describing праздниках, and it has to match it in:

• number: plural
• case: prepositional
• gender: plural has no separate gender distinction

The dictionary form is семейный. In the prepositional plural, it becomes семейных.

So the phrase is:

• на семейных праздниках

Both words are in the same grammatical form:

• семейных = adjective, prepositional plural
• праздниках = noun, prepositional plural

Все here means everyone / all the people.

Even though English often uses singular grammar with everyone, Russian often treats все as a plural group when talking about what the people do:

• все здороваются
• все обнимаются
• все садятся

So the verbs are in the 3rd person plural.

A good way to feel it is:

• все = all of them / everybody

That is why you get plural verb forms, not singular ones.

They organize the sequence of actions.

• сначала = first / at first
• потом = then / afterwards
• только потом = only then / only after that

So the sentence is structured as a clear order:

1. first, people greet each other
2. then, they hug
3. only then, they sit down at the table

Только потом adds emphasis: not just then, but only then.

Because these are reflexive verbs:

• здороваться = to greet / say hello
• обниматься = to hug

The -ся ending often marks a reflexive or reciprocal meaning. In this sentence, the meaning is mostly reciprocal:

• здороваются = greet each other
• обнимаются = hug each other

So this is not really they greet themselves or they hug themselves. It means the people in the group are doing this with one another.

Because in Russian, these reflexive verbs can already imply the social action without naming the other person directly.

For example:

• Все здороваются = Everyone says hello / greets each other
• Все обнимаются = Everyone hugs / hugs each other

If needed, Russian can specify the other person, but very often it does not, because the situation already makes it clear.

This is very natural in Russian when talking about group behavior.

Because садятся means sit down, while сидят means are sitting.

That difference is important:

• садиться = to sit down, to take a seat
• сидеть = to be sitting, to sit

In this sentence, the idea is the change of action:

1. they greet
2. they hug
3. then they sit down at the table

So садятся is exactly the right verb.

Because садиться за стол is a fixed and very common Russian expression meaning to sit down at the table.

Literally, за стол is behind/to the table, but idiomatically it means take a place at the table.

Compare:

• садиться за стол = sit down at the table
• сидеть за столом = be sitting at the table

Notice the case difference:

• за стол = accusative, used with motion / change of position
• за столом = instrumental, used with location

So here:

• садятся за стол = they sit down at the table

Because in Russian, the present tense is often used for habitual or general repeated actions, just like in English:

• На семейных праздниках все сначала здороваются...

This means something like:

• At family celebrations, people first greet each other...

So it is not necessarily describing what is happening right now. It describes what usually happens.

This is a very normal use of the present tense in Russian.

Because the sentence describes a customary sequence of actions, not one completed event with focus on the result.

The verbs are:

• здороваются
• обнимаются
• садятся

These are imperfective forms used in the present tense to describe what people normally do at family celebrations.

In Russian, the present tense is only formed from imperfective verbs. That is one reason you see these forms here.

So the sentence is about a repeated social routine, not a single completed occasion.

The word order is natural and helps emphasize the sequence:

• На семейных праздниках = sets the scene first
• все = says who does the actions
• сначала / потом / только потом = clearly marks the order

Russian word order is more flexible than English, but this version sounds very natural because it presents the information step by step.

If you changed the order, the basic meaning could stay the same, but the emphasis might shift. For example, moving только потом could weaken or change the focus.

So the word order here is doing a stylistic job: it makes the sequence sound clear and natural.