Learn Russian: Вечером мы смотрим фильм.

You are right that the accusative case often changes endings, such as changing feminine words to end in -у. However, for masculine inanimate objects (things that are not alive, like фильм), the accusative form is exactly the same as the dictionary form.

Why is the word for "evening" written as вечером instead of just вечер?

Вечер is the noun "evening". When you want to say "in the evening" (to answer the question "when?"), Russian adds the ending -ом to make it вечером. You will learn this as a set pattern for times of day, like утром for "in the morning".

The dictionary form of the verb "to watch" is смотреть, so why does "we watch" end in -им (смотрим) instead of -ем?

Russian verbs fall into two main conjugation groups for their endings. Even though смотреть ends in -еть, it is a famous exception that belongs to the second group (which usually contains verbs ending in -ить). Because of this, it uses the -им ending for "we" instead of -ем.

Is it okay to change the word order and say: Мы смотрим фильм вечером?

Yes, you absolutely can! Russian word order is very flexible. Putting вечером at the very beginning of the sentence just emphasizes the time, exactly like saying "In the evening, we watch a film" rather than "We watch a film in the evening" in English.