Learn Swedish: Början av filmen är mycket spännande. - The beginning of the film is very exciting.

In Swedish, av is used to express parts of a whole, such as the beginning, middle, or end of something. So "the beginning of the film" is naturally expressed as början av filmen.

Is början in the definite form ("the beginning") here?

Yes! The word en början (a beginning) belongs to a special group of nouns ending in -an. These words usually look exactly the same in their definite form, so början works as both "a beginning" and "the beginning".

Could I say filmens början instead?

Yes, filmens början uses the genitive -s (the film's beginning) and means exactly the same thing. However, using av is very common and often feels a bit more natural in everyday speech when talking about structural parts of a whole, like a book or a movie.

If the subject was an ett word, would spännande get a -t at the end?

No, it wouldn't change. Spännande (exciting) is a present participle, which is a verb form acting as an adjective. Because it ends in -ande, it is indeclinable, meaning it never changes form, no matter if the noun is an en word, an ett word, or plural.