Эта ария была такой красивой, что зрители долго аплодировали.

Эта means this. It has to agree with ария in gender, number, and case.

• ария is feminine
• it is singular
• here it is in the nominative case because it is the subject of the sentence

So the correct form is эта ария = this aria.

Была is the past tense, feminine singular form of быть.

Because ария is a feminine singular noun, the past-tense verb agrees with it:

• он был = he was
• она была = she was
• оно было = it was
• они были = they were

So Эта ария была... means This aria was...

They are in the instrumental feminine singular form.

After была, Russian often uses the instrumental for the predicate adjective or description:

• ария была красивой
• она была интересной
• опера была великолепной

So in this sentence:

• такой agrees with the same feminine singular instrumental pattern
• красивой also agrees with ария

That is why you get такой красивой.

A learner should also know that такая красивая can exist in Russian too, but была такой красивой is a very natural pattern.

This is a very common Russian pattern meaning so ... that.

So:

• такой красивой, что... = so beautiful that...

The second part, introduced by что, gives the result:

• Эта ария была такой красивой, что зрители долго аплодировали.
• The aria was so beautiful that the audience applauded for a long time.

Yes, but the structure would be a little different.

Russian can say:

• так красива, что...
• так красиво, что...
• такой красивой, что...

In your sentence, такой красивой works as an agreeing descriptive phrase after была. It is a very natural way to say so beautiful here.

So a rough comparison is:

• так = so
• такой = often part of an agreeing phrase that also gives the sense of such / so

Russian often uses a regular plural noun where English prefers a collective singular.

• зрители literally means spectators or audience members
• in natural English, you often translate it simply as the audience

So Russian is focusing on the people individually as a group:

• зрители аплодировали = the audience applauded

You could also see words like публика in other contexts.

Долго is an adverb meaning for a long time or for a long while.

It modifies аплодировали:

• долго аплодировали = applauded for a long time

English often uses a whole phrase, while Russian can express it with the single adverb долго.

Because the sentence emphasizes the duration of the action.

Аплодировали is imperfective, which fits very well with долго:

• долго аплодировали = they were applauding for a long time

If you used a perfective verb, the meaning would shift. For example:

• зааплодировали = started applauding
• поаплодировали = applauded for a while

So the imperfective is the most natural choice when the point is that the applause lasted a long time.

Not necessarily. It can be used without an object, just like to applaud in English.

So:

• зрители аплодировали = the audience applauded

If you want to say applaud someone, Russian usually uses the dative case:

• аплодировать певцу = to applaud the singer
• аплодировать артистам = to applaud the performers

In your sentence, no object is needed because the context already makes it clear what they were applauding.

No, Russian word order is fairly flexible.

The given order is natural and neutral:

• Эта ария была такой красивой, что зрители долго аплодировали.

But other orders are possible, depending on emphasis:

• Зрители долго аплодировали, потому что эта ария была такой красивой.
• Эта ария была такой красивой, что долго аплодировали зрители.
  This sounds more marked or literary.

In the original sentence, putting Эта ария first makes the aria the main topic, and the second clause gives the result.