Нам было не до сна, поэтому мы допили чай и ещё раз проверили документы.

It is an idiomatic expression meaning not in the mood for sleep, too occupied to sleep, or sleep was the last thing on our minds.

Literally, не до X means something like it is not the time for X or one is not up to X. So:

• не до сна = not up for sleep / not in a sleeping mood
• мне не до шуток = I’m not in the mood for jokes
• ему сейчас не до разговоров = he’s not up for talking right now

So this sentence does not simply mean we were not sleeping. It suggests they were too worried, busy, or tense to think about sleep.

Because this is an impersonal construction.

Russian often uses the dative case to show the person experiencing a state. Here, нам means to us or for us:

• Нам было не до сна = For us, it was not the time for sleep / We were in no mood to sleep

Compare:

• Мне холодно = I am cold
• Ему скучно = He is bored
• Нам было не до сна = We were not in the mood for sleep

English uses a personal subject (we), but Russian often uses a dative experiencer instead.

Было is the past tense of быть, and in this sentence it is used in an impersonal way.

In Russian impersonal past constructions, the verb is often in the neuter singular form:

• было трудно = it was difficult
• было холодно = it was cold
• нам было не до сна = we were not in the mood for sleep

So было does not agree with нам. It stays in the default impersonal neuter singular form.

Because the expression is не до + genitive.

The noun after до takes the genitive case, so:

• сон → сна
• шутки → шуток
• разговоры → разговоров

That is why we get:

• не до сна
• не до шуток
• не до разговоров

So сна is the genitive singular form of сон.

Допили is the perfective past plural of допить, meaning to finish drinking something that was already being drunk.

So:

• пили чай = were drinking tea / drank tea
• выпили чай = drank the tea
• допили чай = finished the remaining tea

The prefix до- often gives the idea of doing something to the end or finishing what was left.

In this sentence, допили чай suggests they had already been drinking tea, and then they finished it.

Yes, but the nuance changes.

• выпили чай = drank the tea
• допили чай = finished off the tea

Допили is more specific: it emphasizes completion of something already in progress or something partly consumed.

So if the speaker wants to suggest there was tea left, and we finished it, допили is the better choice.

Because проверили is perfective, and here the action is presented as completed.

• проверили документы = checked the documents and finished checking them
• проверяли документы = were checking the documents / used to check the documents

In this sentence, the speaker is describing a sequence of completed actions:

1. допили чай
2. ещё раз проверили документы

That is why perfective verbs fit naturally here.

Ещё раз means once more, one more time, or again.

So:

• ещё раз проверили документы = checked the documents one more time

This expression is very common:

• Скажи ещё раз. = Say it again.
• Прочитай ещё раз. = Read it one more time.

It is often more neutral and precise than опять.

Both can often be translated as again, but they are not always the same.

• ещё раз = one more time, with emphasis on repetition as a counted event
• опять = again, often just meaning repetition, and sometimes it can sound emotional or even annoyed depending on context

Compare:

• Проверь ещё раз. = Check one more time.
• Ты опять проверяешь документы? = Are you checking the documents again?

In your sentence, ещё раз is the natural choice because it means they checked the documents one additional time.

Both are in the accusative case, because they are direct objects.

• допили чай
• проверили документы

However, their forms look like the nominative because they are inanimate:

• masculine inanimate singular: accusative = nominative
  
  • чай → чай
• plural inanimate: accusative = nominative
  
  • документы → документы

So the case is accusative, even though the forms do not change.

Because поэтому introduces the result in a new clause, and the sentence contains two parts:

• Нам было не до сна
• поэтому мы допили чай и ещё раз проверили документы

In standard Russian punctuation, a comma is used here to separate the clauses.

So the structure is:

• cause/state: Нам было не до сна
• result: поэтому мы...

It is very natural here, though it could sometimes be omitted in context.

Russian often omits subjects when they are clear, but in the past tense the verb form допили only shows plural, not specifically we. It could also mean they if the context allowed it.

So мы helps make the subject explicit:

• поэтому мы допили чай... = clearly so we finished the tea...

Without мы, the sentence might still be understood from context, but including it is normal and clear.

Because the word is pronounced with yo, not plain e:

• ещё = pronounced roughly ish-CHO

In many Russian texts, ё is often written simply as е, so you may also see еще. But the correct pronunciation is still ещё.

For learners, it is helpful when ё is written, because it removes ambiguity.