Sinemada yeni filmi izleyenler onu çok beğendi.

A natural breakdown is:

• Sinemada = at/in the cinema
• yeni filmi = the new film as the object of watch
• izleyenler = those who watched / the people who watched
• onu = it
• çok beğendi = liked very much

So the sentence means something like:

• The people who watched the new film at the cinema liked it very much.

The subject is the whole phrase sinemada yeni filmi izleyenler.

Because -da / -de is the locative ending, meaning in / at / on.

• sinema = cinema
• sinemada = in/at the cinema

By contrast:

• sinemaya = to the cinema

So here the sentence is talking about where they watched the film, not motion toward the cinema.

Because it is the definite direct object of izlemek (to watch).

• film = film
• filmi = the film as a specific object being watched

In Turkish, a definite/specific direct object usually takes the accusative ending.

So:

• yeni film izleyenler would sound more like people who watch a new film / some new film
• yeni filmi izleyenler means people who watched the new film, a specific one

The -i here is the accusative marker.

İzleyenler is built like this:

• izle- = watch
• -yen / -en = participle ending, roughly who ... / that ...
• -ler = plural

So:

• izleyen = the one who watches / watched
• izleyenler = those who watch / watched

In this sentence, it means those who watched.

This is a very common Turkish way to say people who do/did X without using a separate word for who.

Great question. The -en / -an participle does not always match English present tense exactly.

It often describes a noun by an action associated with it:

• gelen adam = the man who comes / came / is coming, depending on context
• izleyenler = those who watch / watched / are watching, depending on context

Here the main verb is beğendi (liked), which is past tense, so English naturally uses:

• those who watched

So the time reference is often understood from the whole sentence, not just from -en by itself.

Because Turkish usually uses a participle instead of a relative pronoun like who, which, or that.

English:

• the people who watched the film

Turkish:

• filmi izleyenler
• literally: film-the watching-ones

So Turkish often compresses relative clauses into a single modifier before the noun, or even into a noun-like form such as izleyenler = those who watched.

Onu usually means him / her / it as a direct object.

Here it most naturally means it, referring back to yeni film.

So:

• yeni filmi izleyenler = the people who watched the new film
• onu çok beğendi = liked it very much

Turkish often uses a pronoun like this to avoid repeating the noun.

Because onu is the accusative/object form of o.

• o = he / she / it / that
• onu = him / her / it / that, when it is the direct object

Since beğenmek takes a direct object, Turkish uses onu:

• Onu beğendi = He/She liked it

Using just o here would be wrong, because o is not the object form.

Because in Turkish, when the subject is an explicit third-person plural noun, the verb is often left in the third-person singular form.

So this is normal:

• Öğrenciler geldi = The students came
• İzleyenler beğendi = The viewers liked it

You may also hear:

• İzleyenler onu çok beğendiler

That is also possible. The plural verb ending -ler is often optional when the plural subject is already clearly stated.

So:

• beğendi = very natural
• beğendiler = also possible

Yes. Çok often means very or a lot.

Here it modifies beğendi:

• çok beğendi = liked very much

So it is not saying the film was very liked in a passive sense. It is simply the normal Turkish way to say:

• They liked it a lot
• They liked it very much

In this sentence, it most naturally goes with izleyenler:

• sinemada yeni filmi izleyenler = those who watched the new film at the cinema

So the location is understood as the place of watching.

In theory, word order and context can create other interpretations in Turkish, but here the most natural reading is clearly:

• they watched the film at the cinema
• and then they liked it very much

Yes, Turkish word order is flexible, but changing it usually changes focus or emphasis, not the core meaning.

This version is neutral and natural:

• Sinemada yeni filmi izleyenler onu çok beğendi.

You could also say:

• Onu sinemada yeni filmi izleyenler çok beğendi.

That puts more focus on onu (it).

Or:

• Sinemada yeni filmi izleyenler çok beğendi onu.

That is less neutral and more marked in style, but still understandable.

So the original sentence is a good standard order.

You could, but the meaning would change.

• yeni filmi izleyenler = those who watched the new film
  a specific film

• yeni film izleyenler = those who watch/watched a new film
  less definite, more general or less clearly specific

Since the sentence later says onu (it), the specific version filmi fits better. It clearly points to one particular film that they watched and then liked.