Вчера я так и не дочитала книгу и не дописала письмо преподавательнице.

Because in the past tense, Russian verbs agree with the speaker’s gender and number.

Here the subject is я, and the speaker is understood to be female, so the past tense form is -ла:

• дочитал / дописал = a male speaker
• дочитала / дописала = a female speaker
• дочитали / дописали = plural

Unlike English, я itself does not show gender, but the past-tense verb does.

Так и не adds the idea of in the end not, never did, or still didn’t, despite expectation.

So:

• не дочитала = did not finish reading
• так и не дочитала = still did not finish reading / never ended up finishing reading

It often implies that there was some expectation, intention, or opportunity, but the action remained unfinished.

In this sentence, так и не applies naturally to both verbs:

• she never got around to finishing the book,
• and she never got around to finishing the letter either.

Because до- often gives the meaning finish doing something up to the end.

So:

• читать = to read
• дочитать = to finish reading
• писать = to write
• дописать = to finish writing

This is why the sentence is about not completing the book and the letter, not just about reading or writing in general.

Russian often uses the perfective in negative sentences when the meaning is failed to complete a whole action.

Here the point is not simply that she was not reading or writing. The point is that she did not manage to finish two actions:

• не дочитала книгу = did not finish the book
• не дописала письмо = did not finish the letter

If you used the imperfective instead, the meaning would shift. For example:

• не читала книгу = was not reading / did not read the book
• не писала письмо = was not writing / did not write the letter

So the perfective is used because the sentence is about an unreached result.

They are the direct objects of the verbs.

• дочитать что? → книгу
• дописать что? → письмо

That is why they are in the accusative case.

For these two nouns:

• книга → книгу
• письмо → письмо

Письмо looks the same in nominative and accusative because it is a neuter inanimate noun.

Because преподавательнице is in the dative case, meaning to the female teacher / instructor.

The noun is linked to письмо:

• письмо преподавательнице = a letter to the female teacher

So this is not the object of дописала directly. The direct object is письмо, and преподавательнице tells you who the letter is for.

Base form:

• преподавательница = female teacher / female instructor

Dative form:

• преподавательнице = to the female teacher

Because Russian often expresses this idea through case alone.

English says:

• a letter to the teacher

Russian says:

• письмо преподавательнице

The dative ending already carries the meaning of to. No extra preposition is needed.

In Russian, не normally goes directly before the verb it negates.

So here:

• не дочитала
• не дописала

Each verb is separately negated, and that is the most natural structure.

Also, when two verbs are joined by и, Russian can repeat не with both verbs:

• не дочитала книгу и не дописала письмо

That sounds natural and clear.

Because the subject is the same for both verbs, so Russian usually says it only once.

• Вчера я так и не дочитала книгу и не дописала письмо преподавательнице.

The subject я applies to both дочитала and дописала.

You could repeat it for emphasis, but normally you would not:

• Вчера я так и не дочитала книгу и я не дописала письмо...

That sounds heavier and less natural unless you are stressing the subject.

Grammatically it stands right before дочитала, but in this sentence it is very naturally understood as coloring the whole coordinated idea.

So the meaning is essentially:

• I still didn’t finish the book and didn’t finish the letter either

If a speaker wanted to make the same emphasis explicit for both verbs, they could say:

• Вчера я так и не дочитала книгу и так и не дописала письмо преподавательнице.

But the original version is perfectly natural and does not sound incomplete.

Russian word order is flexible, and putting вчера first sets the time frame right away:

• Вчера = yesterday

Beginning the sentence with it gives something like:

• As for yesterday...
• Yesterday, I...

This is very common in Russian. Other word orders are possible, but Вчера at the start sounds natural and neutral.

Yes, quite likely.

Compare:

• не дочитала книгу = did not finish the book
• не дописала письмо = did not finish the letter

But:

• не читала книгу = was not reading the book / did not read the book
• не писала письмо = was not writing a letter / did not write the letter

The original sentence is specifically about unfinished actions, not simply the absence of those actions.

• преподаватель = teacher / instructor, often masculine in form, but sometimes used more generally depending on context
• преподавательница = female teacher / female instructor

In this sentence, преподавательнице makes it clear that the recipient of the letter is a woman.

A learner should also know that some feminine profession words are more common in some contexts than others, but преподавательница is a normal, understandable word.

That is close in structure, but так и не is a nuance that English often translates more naturally than literally.

Possible natural English equivalents are:

• Yesterday I still didn’t finish the book and didn’t finish the letter to my teacher.
• Yesterday I never got around to finishing the book or the letter to my teacher.
• Yesterday I ended up not finishing the book or the letter to my teacher.

So a very literal translation may sound a little awkward in English, even though it reflects the Russian structure well.