Было уже за полночь, а я всё ещё не могла заснуть без книги.

Было is used because this is an impersonal expression of time.

In Russian, when you say things like:

• Было поздно = It was late
• Было жарко = It was hot
• Было уже за полночь = It was already past midnight

there is no real grammatical subject, so Russian normally uses neuter singular past tense: было.

So было here does not agree with полночь. It is just the standard impersonal form.

Literally, за полночь means something like past midnight or beyond midnight.

• уже = already
• за полночь = past midnight

So the phrase means it was already after midnight.

This is a common Russian way to talk about time being past some point:

• Ему за сорок = He is over forty
• Было за полдень = It was past noon
• Было за полночь = It was past midnight

Here, за takes the accusative case in the meaning of past / beyond a certain point.

So in за полночь, полночь is in the accusative.

However, this is a slightly tricky example because полночь is a feminine noun whose nominative and accusative singular look the same:

• nominative: полночь
• accusative: полночь

So the form does not change, even though the case function does.

А often links two parts of a sentence with a contrast or switch of focus.

Here:

• Было уже за полночь = It was already past midnight
• а я всё ещё не могла заснуть без книги = and yet I still couldn’t fall asleep without a book

So а suggests something like:

• while
• but
• and yet

It is not as strong as но, but it does show contrast. The idea is: It was already past midnight, and yet I still couldn’t fall asleep without a book.

No. In the expression всё ещё, всё does not mean everything.

The phrase всё ещё is a fixed expression meaning still.

So:

• я всё ещё не могла заснуть = I still couldn’t fall asleep

You can think of it as adding emphasis: the situation continued longer than expected.

Compare:

• ещё = still / yet / more, depending on context
• всё ещё = still, with a stronger sense of continuation

Because заснуть means to fall asleep, not to sleep.

• спать = to be sleeping / to sleep
• заснуть = to fall asleep

So:

• не могла заснуть = could not fall asleep

That matches the idea that the speaker was trying to get to sleep, but could not.

If you said не могла спать, that would usually mean couldn’t sleep in a broader sense, often because something prevented sleep in general.
But не могла заснуть focuses specifically on the moment of getting to sleep.

Заснуть is perfective because falling asleep is viewed as a completed transition: you either manage to fall asleep or you don’t.

After мочь (to be able / can), Russian often uses:

• a perfective infinitive if the speaker means manage to do something successfully
• an imperfective infinitive if the speaker means be able to do something in general / be engaged in doing it

Here, не могла заснуть means: I was unable to succeed in falling asleep.

That is why the perfective verb fits well.

Могла is the feminine singular past tense of мочь.

Russian past tense agrees with the subject in gender and number:

• я мог = I could / I was able to (male speaker)
• я могла = I could / I was able to (female speaker)
• мы могли = we could

So могла tells you that the speaker is female.

Because the preposition без always takes the genitive case.

So:

• книга = book
• без книги = without a book

This is a very common pattern:

• без сахара = without sugar
• без воды = without water
• без меня = without me

So книги is genitive singular.

Literally it means without a book, but in context it often implies something like:

• without having a book with me
• without reading a book
• without a book as part of my bedtime routine

Russian often leaves that kind of detail unstated if it is obvious from context.

So не могла заснуть без книги most naturally suggests: the speaker was used to a book being necessary in order to fall asleep.

Yes, Russian word order is fairly flexible, but changing it changes the emphasis.

The given sentence:

Было уже за полночь, а я всё ещё не могла заснуть без книги.

sounds natural and balanced.

If you move things around, the meaning stays mostly the same, but the focus shifts. For example:

• Я всё ещё не могла заснуть без книги, хотя было уже за полночь.
  More emphasis on the speaker’s inability to fall asleep.

• Без книги я всё ещё не могла заснуть.
  Stronger emphasis on without a book.

So the original order is not random: it presents the time first, then contrasts it with the speaker’s continuing inability to fall asleep.

Yes, in many contexts уснуть and заснуть are very close, and both can mean to fall asleep.

So не могла уснуть would also be natural.

A rough distinction is that заснуть can sometimes feel a bit more like drift off / fall asleep, while уснуть is the more neutral fall asleep, but in a sentence like this the difference is small.

So for a learner, the important point is: both are possible, and both are common.