Иногда новый фильм оказывается интереснее, чем кажется сначала.

Here оказывается means turns out to be or proves to be.

It comes from the verb оказываться / оказаться. In this sentence, it does not mean something like finds itself. It is a very common Russian verb for unexpected results:

• Фильм оказывается интересным. = The film turns out to be interesting.
• Это оказалось правдой. = It turned out to be true.

So новый фильм оказывается интереснее... means a new film sometimes turns out to be more interesting...

Because новый фильм is the subject of the sentence.

The sentence is about the new film doing something: it turns out to be more interesting. Subjects are normally in the nominative case in Russian.

• новый = masculine singular nominative adjective
• фильм = masculine singular nominative noun

They match because the adjective agrees with the noun.

Интереснее is the normal comparative form of интересный and means more interesting.

Russian often uses a one-word comparative:

• интересный = interesting
• интереснее = more interesting

This is very common and natural. In this sentence, интереснее works perfectly after оказывается.

A form with более is also possible in some contexts:

• более интересный = more interesting

But here интереснее is the more natural choice.

No. Comparative forms like интереснее do not change for gender, number, or case.

That is different from regular adjective forms. For example:

• интересный фильм
• интересная книга
• интересное письмо

But the comparative stays the same:

• фильм интереснее
• книга интереснее
• письмо интереснее

So интереснее is invariable here.

Чем means than in comparisons.

So:

• интереснее, чем... = more interesting than...

In this sentence:

• интереснее, чем кажется сначала = more interesting than it seems at first

This is the standard Russian way to make this kind of comparison.

Because the subject is understood from context.

The full idea is:

• новый фильм оказывается интереснее, чем он кажется сначала

Russian often omits a repeated subject when it is obvious, especially after чем. So он is not necessary.

Here кажется still refers to the film:
than it seems at first

Here кажется means seems.

It comes from казаться = to seem / to appear.

So:

• кажется сначала = seems at first

Together with the comparison:

• интереснее, чем кажется сначала = more interesting than it seems at first

Сначала is an adverb meaning at first or initially.

It is written as one word here because it functions as an adverb.

Compare:

• сначала = at first
• с начала = from the beginning

These are different expressions:

• Сначала фильм скучный, но потом лучше. = At first the film is boring, but later it gets better.
• С начала фильма я ничего не понял. = From the beginning of the film I understood nothing.

So in your sentence, сначала means at first.

Because the sentence expresses a general truth or something that sometimes happens.

• Иногда = sometimes
• оказывается = present tense

So the sentence means something like:
Sometimes this happens: a new film turns out to be more interesting than it seems at first.

If you used оказался, that would refer to one specific film in the past:

• Новый фильм оказался интереснее, чем казалось сначала.
  = The new film turned out to be more interesting than it seemed at first.

Because чем кажется сначала is a clause introduced by чем.

Russian normally uses a comma before this kind of comparative clause:

• интереснее, чем кажется сначала

This is standard punctuation.

Yes, Russian word order is fairly flexible, though the original version is very natural.

Original:

• Иногда новый фильм оказывается интереснее, чем кажется сначала.

You could also hear:

• Новый фильм иногда оказывается интереснее, чем кажется сначала.
• Иногда новый фильм оказывается интереснее, чем сначала кажется.

These versions are all understandable, but they may shift emphasis slightly.

The original sounds smooth and neutral:

• Иногда sets the general time frame first
• новый фильм introduces the subject
• оказывается интереснее gives the main point
• чем кажется сначала completes the comparison

Russian has no articles.

So новый фильм can mean:

• a new film
• the new film

The exact meaning depends on context.

In this sentence, English usually uses a new film because the statement is general:

• Sometimes a new film turns out to be more interesting than it seems at first.

Here новый simply means new.

It agrees with фильм:

• новый фильм = new film

Depending on context, новый can mean:

• newly released
• newly encountered
• another/new one

But in this sentence, the basic meaning new is enough.