Она стала великой актрисой.

Because the verb is in the past tense, and in Russian past tense verbs agree with the subject in gender and number.

• он стал = he became
• она стала = she became
• оно стало = it became
• они стали = they became

Since она means she, the correct form is стала.

Because after the verb стать in the meaning to become, Russian normally uses the instrumental case.

So:

• dictionary form: великая актриса
• after стала: великой актрисой

This is a very common pattern:

• Он стал врачом = He became a doctor
• Она стала учительницей = She became a teacher
• Она стала великой актрисой = She became a great actress

It is the instrumental singular feminine.

Breakdown:

• великая → великой
• актриса → актрисой

Both words must match in:

• gender: feminine
• number: singular
• case: instrumental

In Russian, when стать means to become, the noun or adjective describing what someone became is usually put in the instrumental.

This is just a standard grammar pattern, and it is worth memorizing:

• стать врачом
• стать известным
• стать хорошим человеком
• стать великой актрисой

So English uses become + noun/adjective, while Russian often uses стать + instrumental.

They are an aspect pair:

• стать = perfective
• становиться = imperfective

In this sentence, стала is from стать, so it presents the change as a completed event: she became a great actress.

Compare:

• Она стала великой актрисой = She became a great actress
• Она становилась великой актрисой = She was becoming a great actress / used to become...
  This is much less natural in most contexts and would need a special situation.

Usually, when talking about a finished result, Russian prefers стать.

Because великий here means great in the sense of famous, outstanding, remarkable, not big in physical size.

So:

• великая актриса = a great actress
• большая актриса would usually sound like a big actress, which is not the intended meaning

Russian often uses великий for greatness in achievement, importance, or historical significance:

• великий писатель = a great writer
• великий ученый = a great scientist

Yes, often it can.

Russian frequently drops subject pronouns when the subject is clear from context. So:

• Она стала великой актрисой
• Стала великой актрисой

Both can work, depending on context.

Including она can:

• make the subject explicit
• add contrast, as in She became a great actress, but her sister did not
• help when the listener might not know who is being talked about

Russian has no articles, so there is no direct equivalent of a or the.

So великой актрисой can mean:

• a great actress
• sometimes the great actress, depending on context

English needs an article, but Russian does not.

Both are possible, but актрисой is the more common modern form.

For many feminine nouns in the instrumental singular, Russian allows:

• -ой
• -ою

So:

• актрисой = common, neutral, standard
• актрисою = also correct, often more literary or poetic in tone

The same applies to the adjective:

• великой
• великою

But in normal modern usage, Она стала великой актрисой is the most natural version.

The neutral word order is:

• Она стала великой актрисой

This is the most straightforward way to say it.

But Russian word order is flexible and can change for emphasis:

• Великой актрисой она стала = It was as a great actress that she became known / A great actress she became
• Стала она великой актрисой = more marked, often stylistic or contrastive

So the original sentence has the most neutral, standard order.

A simple pronunciation guide:

• великой ≈ vee-LYE-kay
• актрисой ≈ ak-TREE-say

The stress is on:

• вели́кой
• актри́сой

So the full sentence is approximately:

• аНА staLA vee-LYE-kay ak-TREE-say

A more accurate stress pattern is:

• Она́ стала велико́й актри́сой

Stress matters in Russian, so it is useful to learn the stressed syllables together with the word.