Этот фильм заслуживает внимания.

Because фильм is a masculine singular noun, and the demonstrative this has to agree with it.

• masculine singular: этот
• feminine singular: эта
• neuter singular: это
• plural: эти

So:

• этот фильм = this film
• эта книга = this book
• это письмо = this letter

A useful point: это can also mean this is in sentences like Это фильм = This is a film, but that is a different use.

Because the verb заслуживать / заслужить commonly takes a direct object in the genitive case when the noun is something abstract, and внимание is one of the very common words used this way.

So:

• dictionary form: внимание
• in the sentence: внимания = genitive singular

This pattern is very common:

• заслуживать уважения = to deserve respect
• заслуживать доверия = to deserve trust
• заслуживать внимания = to deserve attention

So even though English says deserve attention, Russian uses the genitive here.

Заслуживает is the 3rd person singular present tense form of заслуживать.

It means deserves.

Breakdown:

• infinitive: заслуживать = to deserve
• он / она / оно заслуживает = he/she/it deserves

Since фильм is singular, the verb is also singular:

• Этот фильм заслуживает... = This film deserves...

Yes. Заслуживать is the imperfective verb.

Its common perfective partner is заслужить.

• заслуживать = to deserve, to be deserving of
• заслужить = to earn, to deserve as a completed result

Examples:

• Этот фильм заслуживает внимания. = This film deserves attention.
  (general statement, imperfective)

• Он заслужил уважение коллег. = He earned the respect of his colleagues.
  (completed result, perfective)

In your sentence, the imperfective is natural because it describes a general quality of the film.

Because in the present tense, Russian usually does not use a word for is / are / am.

So English:

• This film is worthy of attention
• This film deserves attention

can be expressed in Russian without a present-tense to be.

The whole predicate is carried by заслуживает = deserves, so there is no missing word.

Yes, Russian word order is relatively flexible, though the most neutral version here is:

• Этот фильм заслуживает внимания.

You could also say:

• Внимания заслуживает этот фильм.

That version puts more emphasis on внимания or makes the sentence sound more stylistically marked, as if answering Which film deserves attention?

For a learner, the original order is the safest and most natural neutral choice.

Not in standard Russian. After заслуживает, you normally need the noun in the genitive:

• внимания

If you want to specify whose attention, you also put that word into the genitive:

• Этот фильм заслуживает вашего внимания. = This film deserves your attention.

So:

• внимание → nominative
• внимания → genitive
• ваше внимание → nominative
• вашего внимания → genitive

The standard stresses are:

• этот
• фи́льм
• заслу́живает
• внима́ния

A rough pronunciation guide:

• Э́тот фи́льм заслу́живает внима́ния.

For English speakers, the important thing is not to move the stress in заслуживает or внимания, because Russian stress is meaningful and not always predictable.

Not always, but here it matches very well.

Внимание can mean:

• attention
• notice
• focus

In this sentence, it means something like:

• the film is worth noticing
• the film deserves people’s attention
• the film is worth paying attention to

So it is a very natural and idiomatic choice here.

It is mostly neutral to slightly formal/bookish.

You might see it in:

• reviews
• articles
• recommendations
• cultural commentary

In everyday speech, people might also say more conversational things such as:

• Этот фильм стоит посмотреть. = This film is worth watching.
• Фильм хороший, советую. = The film is good, I recommend it.

But Этот фильм заслуживает внимания is perfectly natural and common, especially in writing and reviews.

Этот фильм заслуживает внимания is the standard, idiomatic phrasing.

Этот фильм стоит внимания is generally not the normal way to say it.

Russian usually says:

• заслуживает внимания = deserves attention
• стоит посмотреть = is worth watching
• стоит вашего внимания can occasionally appear, but it is much less standard/basic for learners than заслуживает внимания

So if you want the safest natural expression, use:

• Этот фильм заслуживает внимания.

Yes. That is exactly one of its useful nuances.

Этот фильм заслуживает внимания often means:

• the film is worth checking out
• it should not be ignored
• it has something valuable or interesting about it

It is positive, but not necessarily extreme. It does not automatically mean:

• the film is brilliant
• the film is a masterpiece

It is often a measured, thoughtful kind of praise.