Dziś wieczorem nie mam czasu na obejrzenie filmu.

Because Polish usually drops subject pronouns when they are clear from the verb form.
Here, mam means I have, so ja is unnecessary.

• mam = I have
• nie mam = I do not have

You could say Ja dziś wieczorem nie mam czasu..., but that would add emphasis, like I don’t have time tonight.

Dziś wieczorem means this evening or tonight.

The two words work together:

• dziś = today
• wieczorem = in the evening

So together they narrow the time down to the evening of today.

Because wieczorem is the form used adverbially to mean in the evening.

• wieczór = evening as a noun
• wieczorem = in the evening

This is a very common pattern with parts of the day in Polish. In this sentence, wieczorem is not the subject or object; it functions more like a time adverb.

Because in Polish, negation often causes the object to go into the genitive case.

• positive: mam czas = I have time
• negative: nie mam czasu = I don’t have time

So czas changes to czasu after nie mam. This is a very important Polish pattern.

Because Polish commonly uses the pattern:

mieć czas na + accusative = to have time for + something

So:

• mam czas na film = I have time for a film
• nie mam czasu na obejrzenie filmu = I don’t have time for watching the film / to watch the film

Here na introduces the activity that there is no time for.

Because Polish can express this idea in two common ways:

1. nie mam czasu na obejrzenie filmu
2. nie mam czasu obejrzeć filmu

Both are correct.

The version in your sentence uses na + a verbal noun:

• obejrzenie = watching / viewing, the act of watching to completion

This structure is a bit more noun-like: for the watching of the film.

The infinitive version, nie mam czasu obejrzeć filmu, is also very natural and often feels a bit more direct in everyday speech.

Obejrzenie is a verbal noun made from the verb obejrzeć.

• obejrzeć = to watch / to see, usually with the idea of completing the action
• obejrzenie = watching, viewing, the act of watching

Polish often turns verbs into nouns like this, especially after prepositions such as na.

So na obejrzenie filmu literally means something like for the watching of the film.

This is about aspect, which is very important in Polish.

• oglądać / oglądanie = imperfective, focusing on the process
• obejrzeć / obejrzenie = perfective, focusing on completion

A film is something you often think of as a complete whole, so obejrzenie filmu suggests watching the whole film.

Compare:

• oglądanie filmu = watching a film, the activity/process
• obejrzenie filmu = watching the film through to the end

In this sentence, the perfective form fits well because the speaker means they do not have time to finish watching a film.

Because film depends on the verbal noun obejrzenie, and with this kind of verbal noun, the object usually appears in the genitive case.

So:

• film = nominative
• filmu = genitive

That is why we get:

• obejrzenie filmu = watching the film
• not obejrzenie film

This is a common pattern with verbal nouns in Polish.

Yes. Polish word order is more flexible than English word order.

Your sentence is a natural, neutral version:

Dziś wieczorem nie mam czasu na obejrzenie filmu.

But you could also say:

• Nie mam dziś wieczorem czasu na obejrzenie filmu.
• Na obejrzenie filmu nie mam dziś wieczorem czasu.

These versions are still grammatical, but they change the emphasis a little. Polish often moves words around to highlight different parts of the sentence.

Yes, in most situations they mean the same thing: today.

• dziś = shorter
• dzisiaj = slightly fuller form

Both are very common. In your sentence, you could also say:

Dzisiaj wieczorem nie mam czasu na obejrzenie filmu.

That would mean the same thing.

It can often be understood more generally as a film in English, because Polish has no articles like a and the.

So depending on context, filmu could mean:

• a film
• the film

If no specific film has been mentioned before, English will usually translate it as a film. If both speakers already know which film is meant, then the film may be a better translation.