После учений директор сказала, что эвакуация прошла быстро и без ошибок.

После always takes the genitive case.

So:

• после = after
• base form: учения = drills / exercises
• genitive plural: учений

That is why you get после учений.

A few similar examples:

• после урока = after the lesson
• после работы = after work
• после занятий = after classes

So the pattern is: после + genitive.

The dictionary form is учение or, in this meaning, often учения in the plural.

In Russian, учения very often means drills / exercises / maneuvers, especially in official, military, emergency, or school contexts.

So:

• учения = drills, exercises
• после учений = after the drills / after the exercise session

This is more natural than singular in many real-life contexts. Russian often uses the plural for organized drills.

Many Russian job titles are traditionally masculine in form, even when they refer to a woman.

So a woman can be called:

• директор
• врач
• профессор
• редактор

This is normal Russian usage.

Russian sometimes has specifically feminine forms for professions, but they may sound informal, marked, old-fashioned, or stylistically different. For директор, standard neutral usage is very often still just директор, even for a female director.

Because the verb agrees with the real gender of the person, not just the grammatical shape of the job title.

So here:

• директор = a female director
• therefore: сказала = said (feminine)

This kind of agreement is very common with profession words referring to women:

• врач сказала = the doctor said
• директор решила = the director decided
• профессор объяснила = the professor explained

So the noun may stay masculine in form, but the past-tense verb can still be feminine.

Here прошла is the feminine past tense of пройти.

Literally, пройти often means to pass or to go through, but with events it often means:

• to go
• to proceed
• to take place
• to go off

So:

• эвакуация прошла быстро = the evacuation went quickly

This is a very common Russian pattern with events:

• встреча прошла хорошо = the meeting went well
• экзамен прошёл успешно = the exam went successfully
• концерт прошёл отлично = the concert went great

Because эвакуация is feminine, the verb is прошла.

Because эвакуация is a feminine singular noun.

Past-tense verbs in Russian agree in gender and number:

• masculine: прошёл
• feminine: прошла
• neuter: прошло
• plural: прошли

So:

• эвакуация → feminine
• therefore: эвакуация прошла

Because без takes the genitive case.

The noun is ошибка = mistake/error.

After без, you need genitive:

• singular genitive: ошибки
• plural genitive: ошибок

In this sentence, без ошибок means without mistakes / without any mistakes, which is the most natural choice.

Compare:

• без ошибки = without a mistake / without one mistake
• без ошибок = without mistakes / error-free

Russian often uses the plural here to express the general idea of being mistake-free.

Что introduces a subordinate clause and often means that.

So:

• директор сказала, что... = the director said that...

This is the standard way to report statements in Russian.

More examples:

• Он сказал, что придёт. = He said that he would come.
• Она думает, что это правильно. = She thinks that this is correct.
• Я знаю, что он дома. = I know that he is at home.

In everyday English, that is often omitted, but in Russian что is usually stated clearly.

No, быстро and скоро are different.

• быстро = quickly, fast
• скоро = soon

Here the sentence describes how the evacuation happened, so быстро is correct:

• эвакуация прошла быстро = the evacuation went quickly

If you said скоро, that would sound more like it happened soon, which is a different idea.

Russian word order is fairly flexible, but different orders change the focus or emphasis.

The given sentence:

• После учений директор сказала, что эвакуация прошла быстро и без ошибок.

This order naturally sets the time frame first: After the drills...

You could also say:

• Директор сказала после учений, что эвакуация прошла быстро и без ошибок.

That is also understandable, but it shifts the rhythm and focus slightly.

Putting после учений first is very natural because Russian often begins with context such as time, place, or background.

Because Russian has no articles like a and the.

So:

• директор can mean a director or the director
• эвакуация can mean an evacuation or the evacuation

Russian shows definiteness from context, not from articles.

In this sentence, the context makes it clear that we mean a specific director and a specific evacuation.