Стоит нам сесть за стол, как дети начинают рассказывать о своём дне.

Here стоит is part of a fixed pattern:

Стоит кому-то + infinitive, как ...

It means something like:

• as soon as ...
• the moment ...
• it only takes ... for ... to happen
• no sooner ... than ...

So Стоит нам сесть за стол, как дети начинают... means:

• As soon as we sit down at the table, the children start...
• literally, something like It only takes us to sit down at the table for the children to start...

This is not the normal стоить = to cost, and not стоять = to stand in the usual sense.

Because this construction uses the dative case:

стоит кому? + infinitive

So:

• мне — to me
• тебе — to you
• нам — to us
• детям — to the children

Examples:

• Стоит мне открыть книгу, как он начинает говорить.
  As soon as I open the book, he starts talking.
• Стоит нам выйти, как начинается дождь.
  As soon as we go out, it starts raining.

So нам is required by the grammar of this expression.

Because сесть is perfective and means to sit down, that is, to complete the action of taking a seat.

Compare:

• сидеть — to be sitting
• садиться — to sit down / be in the process of sitting down
• сесть — to sit down and complete that action

In this sentence, the idea is:

the moment we sit down, the children start talking.

So Russian uses сесть, because it marks the completed change into the seated position.

If you said сидеть, it would sound more like while we are sitting or to sit as a state, which is not the intended meaning here.

This is about motion vs. location.

With за:

• за стол (accusative) = to the table / to take a seat at the table
• за столом (instrumental) = at the table, already seated there

Because сесть involves movement into a position, Russian uses за стол.

Compare:

• Мы сели за стол. — We sat down at the table.
• Мы сидим за столом. — We are sitting at the table.

So сесть за стол is the normal phrase for sit down at the table.

Not in this context.

Russian за can mean different things depending on the verb and situation. With verbs like сесть, садиться, усадить, the phrase за стол means to sit down at the table.

So although за often translates as behind, here the whole phrase is idiomatic:

• сесть за стол = sit down at the table
• пригласить за стол = invite to the table
• сидеть за столом = sit at the table

This is just standard Russian usage.

No. In this sentence, как is part of the paired construction:

Стоит ..., как ...

Here it means something like:

• and then immediately
• when suddenly
• as soon as
• than in English no sooner ... than ...

So:

Стоит нам сесть за стол, как дети начинают рассказывать...

means:

No sooner do we sit down at the table than the children start telling us...

This как is not the question word how.

Using начинают рассказывать emphasizes the beginning of the action.

Compare:

• дети рассказывают о своём дне — the children tell us about their day
• дети начинают рассказывать о своём дне — the children start telling us about their day

Because the sentence focuses on what happens immediately after we sit down, the verb начинают fits very naturally: it highlights the instant reaction.

After начинать / начать, Russian usually uses an imperfective infinitive, because the meaning is to begin doing something, that is, to begin a process.

So:

• начинают рассказывать — correct
• начинают читать — correct
• начинают писать — correct

The imperfective verb describes the activity as an ongoing action or process.

Using рассказать here would sound unnatural, because рассказать is perfective and focuses on a completed result: to tell fully / to finish telling.

So the normal choice is:

начинать + imperfective infinitive

Because Russian strongly prefers the reflexive possessive свой when the possession belongs to the subject of the clause.

In the clause:

дети начинают рассказывать о своём дне

the subject is дети, and the day belongs to the children, so Russian uses своём.

Compare:

• Он говорит о своей работе. — He talks about his work.
• Они думают о своих детях. — They think about their children.

If you used их, it could sound less natural and might even create ambiguity, because их can refer to someone else's day depending on context.

So о своём дне is the normal and best choice.

It is prepositional case, because it comes after о in the meaning about.

The phrase is:

• о дне — about the day
• о своём дне — about their own day

Forms of свой here:

• masculine/neuter singular prepositional: своём
• so: о своём дне

This matches дне, which is masculine singular prepositional.

Russian often uses the present tense for habitual, repeated, or general situations.

This sentence describes something that typically happens whenever they sit down at the table. So the present tense means:

• whenever this happens
• this is what usually happens

It is not necessarily about one specific moment right now.

English often does the same:

• As soon as we sit down, the children start talking.

So the present tense here expresses a regular pattern.

Most naturally, it describes a repeated habit or a typical situation.

The meaning is:

Whenever we sit down at the table, the children start talking about their day.

That is because:

• the present tense suggests regularity
• the construction Стоит ..., как ... often describes something that happens reliably and immediately

In the right context, it could describe a vivid present-time scene, but the default reading is habitual.

Yes, it is a normal and fairly common pattern, but it sounds a little more bookish or literary than the most neutral everyday option.

A more neutral everyday alternative would be:

• Как только мы садимся за стол, дети начинают рассказывать о своём дне.

Both are correct, but they differ a bit in style:

• Стоит нам сесть..., как... — a bit more expressive, polished, or written
• Как только... — very common and straightforward in speech

So learners should understand this pattern well, even if they may not use it as often at first.

Yes. A very close equivalent is:

Как только мы садимся за стол, дети начинают рассказывать о своём дне.

or, if you want a slightly different aspectual choice:

Как только мы сядем за стол, дети начинают рассказывать о своём дне.

But the original has a special nuance: Стоит нам сесть..., как... suggests that the second action follows almost automatically and immediately.

So как только is a good practical synonym, but the original sounds a bit more expressive.

Because стоит here is not agreeing with нам as a normal subject.

This construction is essentially impersonal:

стоит кому-то + infinitive

So the verb stays in the fixed third-person singular form:

• Стоит мне...
• Стоит тебе...
• Стоит нам...
• Стоит детям...

It does not change to plural to match нам or детям.

The sentence can be broken down like this:

Стоит + dative + infinitive, как + main clause

In this example:

• Стоит — fixed verb in the construction
• нам — dative, to us
• сесть за стол — infinitive phrase, to sit down at the table
• как — introduces the immediate result
• дети начинают рассказывать о своём дне — main clause

So the pattern is:

As soon as X happens, Y immediately happens.

That is the key grammar idea behind the sentence.