Mog brata zanima novi film.

Because zanimati works like to interest, not like to be interested in.

So the Serbian structure is literally closer to:

The new film interests my brother.

That means:

• novi film = the thing that causes interest
• mog brata = the person being interested

Because my brother is the object here, it appears in the accusative case, not the nominative.

For the noun brat, the accusative singular of an animate masculine noun looks like the genitive:

• nominative: moj brat
• accusative: mog brata

So mog brata is exactly what we expect in this sentence.

Here it is accusative, even though it looks like genitive.

That happens because masculine animate nouns in Serbian often have:

• genitive singular = brata
• accusative singular = brata

The same overlap happens with mog.

So in form, mog brata could be genitive or accusative, but in this sentence it must be accusative because the verb zanimati takes the person affected as its direct object.

The subject is novi film.

A native English speaker may expect my brother to be the subject, because English usually says My brother is interested in the new film. But Serbian often uses a different structure:

• novi film = subject
• zanima = verb
• mog brata = object

So grammatically, the sentence is built like:

The new film interests my brother.

Because it agrees with the subject, and the subject is novi film, which is singular.

In Serbian, present-tense verbs agree with the subject in person and number.

Here:

• subject: novi film = singular
• verb: zanima = 3rd person singular

If the subject were plural, the verb would also be plural:

• Mog brata zanimaju novi filmovi. = My brother is interested in the new films.

Because novi film is in the nominative, since it is the subject.

Breakdown:

• novi = nominative masculine singular
• film = nominative masculine singular

If it were in another case, the form would change. For example, genitive would be novog filma.

So novi film appears here because it is doing the grammatical job of the subject.

Mog is a standard short form of the possessive adjective moj.

For masculine/neuter singular oblique cases, Serbian often allows both a shorter and a longer form:

• mog
• moga

So both of these are possible:

• Mog brata zanima novi film.
• Moga brata zanima novi film.

The shorter form mog is very common and completely normal.

Because Serbian has no articles.

That means Serbian does not have separate words for a/an and the like English does. Context tells you whether novi film means:

• a new film
• the new film

In this sentence, the intended meaning may be the new film, but Serbian does not mark that with an article.

Yes. Serbian word order is relatively flexible because case endings show the grammatical roles.

So all of these are possible, with slightly different emphasis:

• Mog brata zanima novi film.
• Novi film zanima mog brata.

The version with mog brata first often gives a slight emphasis like as for my brother... or keeps the focus on him. The version with novi film first may feel more straightforward in some contexts.

The meaning stays basically the same because the cases still show who is the subject and who is the object.

Very often, yes. Zanimati commonly means to interest, so the thing of interest is the subject, and the person interested is in the accusative.

Examples:

• Mene zanima istorija. = History interests me.
• Njega zanima sport. = Sport interests him.
• Decu zanima muzika. = Music interests the children.

This is one of the most important patterns to get used to, because English usually prefers to be interested in, while Serbian often prefers something interests someone.

Yes. A very common alternative is:

Moj brat je zainteresovan za novi film.

That is closer to English My brother is interested in the new film.

So you can think of the two patterns like this:

• Mog brata zanima novi film.
  Literally: The new film interests my brother.

• Moj brat je zainteresovan za novi film.
  Literally: My brother is interested in the new film.

Both are natural, but the first one is especially useful because it reflects a very common Serbian sentence pattern.