Learn Hardcore Czech: Naše děti se večer nesmí dívat na hlasitý film v televizi. - Our children are not allowed to watch a loud film on TV in the evening.

In Czech, dívat se is a reflexive verb and is learned as a fixed expression. The reflexive particle se is part of the verb; you cannot normally drop it.

dívat se na něco = to watch / to look at something
- Dívám se na film. – I’m watching a film.

Without se, dívat is usually only seen in some derived or archaic uses, not as the normal everyday verb to watch.

There are many such reflexive verbs in Czech where se is just part of the verb’s dictionary form, for example:

smát se – to laugh
učit se – to learn
bát se – to be afraid

So you should memorize dívat se as the whole verb.

What exactly does nesmí mean here? Is it “cannot” or “must not”?

Nesmí expresses prohibition or lack of permission, not physical impossibility.

Naše děti se večer nesmí dívat… = Our children are not allowed to watch… / must not watch…

Compare:

nemůžou se dívat – they cannot watch (they are unable to: no electricity, no TV, they’re too busy, etc.)
nesmí se dívat – they must not / are not permitted to watch (there is a rule or prohibition)

So although English often says can’t watch, the most accurate Czech for a rule is nesmí se dívat.

Is nesmí here singular or plural? How is smět / nesmět conjugated?

In this sentence, nesmí is 3rd person plural (because of naše děti), but the form nesmí is the same for 3rd singular and 3rd plural.

Verb smět (to be allowed to) in the present tense:

já smím / nesmím
ty smíš / nesmíš
on, ona, ono smí / nesmí
my smíme / nesmíme
vy smíte / nesmíte
oni smějí/smí / nesmějí/nesmí

So in 3rd person plural you can say:

Naše děti se večer nesmí dívat…
or (slightly more formal/explicit)
Naše děti se večer nesmějí dívat…

Both are correct; nesmí is more common in everyday speech.

Where should se go? Could I say Naše děti nesmí se večer dívat…?

No, Naše děti nesmí se večer dívat… sounds wrong to native speakers.

The short pronoun se is a clitic: it usually wants to be in second position in the clause (after the first stressed word or phrase). In your sentence that gives:

Naše děti se večer nesmí dívat… – natural
Večer se naše děti nesmí dívat… – also natural

Variants where se is pushed later, like:

Naše děti večer se nesmí dívat…
Naše děti nesmí se večer dívat…

are ungrammatical or at least very unnatural in standard Czech.

So keep se near the beginning, following the first main element of the clause.

Why is it na hlasitý film with na + accusative?

After dívat se you almost always use na with the accusative case to say what you are watching:

dívat se na film – watch a film
dívat se na televizi – watch TV
dívat se na seriál – watch a series

So na hlasitý film is:

na (preposition required by dívat se)
hlasitý film in accusative singular (masculine inanimate)

If film were plural, you would get:

na hlasité filmy – watch loud films (accusative plural)

What case is v televizi? Why does televizi look like accusative?

Here v televizi is locative case, used after v when it means in / inside / on (as a medium).

Noun televize (feminine) has:

nominative: televize
accusative: televizi
locative: televizi

So accusative and locative have the same form: televizi.
In this sentence we know it’s locative because of the preposition v, which in this meaning (in/on TV) always takes the locative:

Viděl jsem to v televizi. – I saw it on TV.

So:

na hlasitý film – what they watch (accusative after dívat se na)
v televizi – where that film is shown (locative after v)

Why is it naše děti and not naši děti?

Possessive pronoun náš (our) changes form according to gender and number of the noun.

The plural nominative forms are:

masculine animate: naši (naši kamarádi – our (male) friends)
all other genders in plural (masc. inanimate, feminine, neuter): naše
- naše knihy – our books (fem.)
- naše auta – our cars (neuter)
- naše města – our cities (neuter)

The noun dítě (child) is neuter singular, but děti (children) behave grammatically like feminine plural. So you must use naše děti, not naši děti.

How does hlasitý agree with film? How would it change with other genders or in plural?

Hlasitý is an adjective that must agree with film in gender, number, and case.

Here we have:

film – masculine inanimate, singular, accusative
the adjective pattern mladý gives hlasitý in this form

So:

nominative: hlasitý film – a loud film
accusative: also hlasitý film (for masculine inanimate, nominative = accusative)

Other examples:

feminine singular: hlasitá hudba (nom./acc.) – loud music
neuter singular: hlasitě rádio (nom./acc.) – loud radio
plural masculine inanimate: hlasité filmy – loud films
plural feminine: hlasité písně – loud songs

In your sentence, hlasitý is masculine singular accusative to match film.

Can večer be moved to another position? Does that change the meaning?

You can move večer quite flexibly; Czech word order is relatively free, and the basic meaning stays the same. Examples:

Naše děti se večer nesmí dívat na hlasitý film v televizi.
– neutral: focuses on the rule, mentions in the evening in the middle.
Večer se naše děti nesmí dívat na hlasitý film v televizi.
– slight emphasis on in the evening (as the time frame).
Naše děti se nesmí večer dívat na hlasitý film v televizi.
– still okay; more emphasis on nesmí (the prohibition).

You would normally avoid splitting se away from the beginning or creating very heavy clusters before the verb. But moving večer among the subject/verb part is generally fine and does not change the core meaning; it only shifts focus slightly.

Why do we have both na hlasitý film and v televizi? What is the difference between na and v here?

They express two different relationships:

dívat se na hlasitý film
- na
  - accusative after dívat se tells you what they are watching (the object of watching).
hlasistý film v televizi
- v
  - locative tells you where / in what medium that film is available (on TV).

So the structure is:

not allowed to watch (dívat se na …)
what: a loud film (na hlasitý film)
where that film is shown: on TV (v televizi)

You could also have sentences like:

Dívám se na film v kině. – I’m watching a film in the cinema.
Dívám se na film na počítači. – I’m watching a film on the computer.

In all of them, na + accusative marks the thing watched, and v/na + locative or other prepositions describe the place or medium.