После финала зрители долго аплодировали и не хотели уходить.

Because после normally requires the genitive case when it means after.

• финал = nominative singular
• финала = genitive singular

So:

• после финала = after the final

This is a very common pattern:

• после урока = after the lesson
• после фильма = after the film
• после концерта = after the concert

Зрители is nominative plural. It is the subject of the sentence, so nominative is used.

Singular and plural:

• зритель = spectator, viewer
• зрители = spectators, viewers

Since the sentence is about multiple people doing the actions, the plural subject matches the plural verbs:

• зрители аплодировали
• зрители не хотели уходить

In the past tense, Russian verbs agree with the subject in number and, in the singular, also gender.

Here the subject is plural: зрители, so both verbs take the plural past ending -ли:

• аплодировал = he applauded
• аплодировала = she applauded
• аплодировало = it applauded
• аплодировали = they applauded

And similarly:

• хотел = he wanted
• хотела = she wanted
• хотели = they wanted

You do not have to name the person or people being applauded. Аплодировать can be used on its own, just like to applaud in English.

So:

• зрители долго аплодировали = the spectators applauded for a long time

If you want to say to whom they applauded, Russian usually uses the dative:

• аплодировали артистам = they applauded the performers
• аплодировали победителю = they applauded the winner

So the sentence is perfectly complete without an object.

Долго is an adverb meaning for a long time. Here it modifies аплодировали.

So the structure is:

• зрители долго аплодировали = the spectators applauded for a long time

It tells you about the duration of the action.

Compare:

• громко аплодировали = applauded loudly
• долго аплодировали = applauded for a long time

This is mainly about aspect.

• уходить = imperfective
• уйти = perfective

After не хотеть, Russian often uses the imperfective when talking about unwillingness to begin or continue an action in a general sense:

• не хотели уходить = they did not want to leave / they were unwilling to leave

This sounds natural because the focus is on their reluctance about the process of leaving, not on reaching the completed result of having left.

If you said не хотели уйти, it would be much less natural here.

They are an aspect pair:

• уходить = imperfective
• уйти = perfective

Very roughly:

• уходить focuses on the process, repetition, or general idea of leaving
• уйти focuses on one completed act of leaving

Examples:

• Он уже уходил, когда я пришёл. = He was already leaving when I arrived.
• Он ушёл. = He left. / He has gone.

In your sentence, уходить fits because the idea is they didn’t want to go away rather than they didn’t want to accomplish the act of having left.

Because Russian infinitives do not use a separate word like English to.

• уходить already means to leave
• хотели уходить literally works as wanted leave, but in correct English we say wanted to leave

This is normal after verbs like хотеть:

• хочу спать = I want to sleep
• хотим поехать = we want to go
• не хотели уходить = did not want to leave

Because both actions are presented as ongoing/background-like rather than single completed events.

• аплодировали is imperfective because the applause lasted for some time, which matches долго
• хотели is imperfective because wanting is a state, and Russian normally uses imperfective here

So the sentence paints a scene:

• after the final, the spectators were applauding for a long time
• and they did not want to leave

This is a very natural use of the imperfective in narration.

Yes. Russian word order is fairly flexible, though the neutral version here is very natural:

• После финала зрители долго аплодировали и не хотели уходить.

You could also say:

• Зрители после финала долго аплодировали и не хотели уходить.

Both are grammatical. The version with После финала first sets the time frame immediately: After the final...

Russian often moves time expressions to the front for context.

Because the same subject applies to both verbs, so Russian does not need to repeat it.

Structure:

• зрители = subject
• аплодировали = first verb
• и не хотели уходить = second verb phrase with the same subject understood

English works the same way:

• The spectators applauded for a long time and did not want to leave.

Repeating the subject would be possible in some contexts, but it would sound unnecessary here.

It is a prepositional phrase giving the time context: after the final.

It does not change the case of the subject or the tense of the verbs. Its main job is to answer when?

Sentence structure:

• После финала = when?
• зрители = who?
• долго аплодировали = what did they do?
• и не хотели уходить = what else did they do / feel?

So it frames the whole sentence but does not control anything except the genitive case of финала.