Я вчера кое-как дочитала черновой отчёт, потому что была очень уставшей.

Дочитала comes from дочитать, which means to finish reading something to the end.

The prefix до- adds the idea of reaching the end of an action. So:

• читала = was reading / read
• прочитала = read through / read completely
• дочитала = finished reading something that had already been started

In this sentence, дочитала suggests that the speaker was working through the draft report and finally got to the end of it.

With кое-как, it gives the sense of I barely managed to finish it.

Кое-как means something like:

• somehow
• with difficulty
• barely
• in a slapdash way

It often suggests that the action was done with effort, not smoothly, and maybe not very well.

So вчера кое-как дочитала means the speaker finished reading it, but only with difficulty, probably because she was tired.

In the past tense, Russian verbs agree in gender and number, not person.

So with я:

• a male speaker says дочитал
• a female speaker says дочитала

That means this sentence is being said by a woman.

Russian often leaves out subject pronouns when the subject is already clear from context.

So:

• Я вчера кое-как дочитала... = I yesterday barely finished reading...
• ..., потому что была очень уставшей = ..., because I was very tired

The я is understood automatically in the second clause. Russian does this much more freely than English.

Черновой отчёт means a draft report or a rough version of a report.

• черновой = draft / rough / preliminary
• отчёт = report

So this is not the final polished version. It is a working draft.

The adjective черновой does not mean black here. It comes from the idea of a rough draft, as opposed to a finished clean version.

Because the word is pronounced with ё, not е:

• отчёт = approximately atch-YOT

In many Russian texts, ё is often written as е, so you may also see отчет. But the pronunciation is still отчёт.

For learners, it is helpful to remember the ё, because it shows both the correct sound and the stress.

After быть, Russian often uses the instrumental case for a predicate noun or adjective.

So:

• была уставшей = was tired

Here уставшей is the feminine singular instrumental form, matching the female speaker.

This pattern is very common:

• он был врачом = he was a doctor
• она была уставшей = she was tired

You may also hear nominative forms like была очень усталая / уставшая, especially in colloquial speech, but была очень уставшей is fully natural and standard.

Both can mean tired, and in many situations they are close.

But there is a slight nuance:

• усталый / усталая = the basic adjective tired
• уставший / уставшая = literally having become tired, so it can feel a bit more result-focused

So была очень уставшей can suggest she had become very tired.

In everyday speech, though, the difference is often small, and native speakers may use both.

No. Вчера by itself does not force perfective aspect.

What matters is the meaning the speaker wants:

• вчера читала отчёт = yesterday I was reading the report
• вчера дочитала отчёт = yesterday I finished reading the report

The sentence describes a completed result, so perfective дочитала is the natural choice.

Yes. Russian word order is flexible, and changing it changes emphasis more than basic meaning.

This version is natural and fairly neutral:

• Я вчера кое-как дочитала черновой отчёт...

Other possible orders:

• Вчера я кое-как дочитала черновой отчёт...
  More emphasis on yesterday

• Кое-как я вчера дочитала черновой отчёт...
  More emphasis on the struggle

So the chosen word order sounds natural, but it is not the only possible one.