Letní kino je dnes otevřené.

Not usually. Letní kino is a fixed expression in Czech.

• Literally, it means summer cinema
• In real usage, it usually means an open-air / outdoor cinema

So it refers to a place or event where films are shown outside, especially in warm weather. It does not normally just mean any cinema during summer.

It is in the nominative case because it is the subject of the sentence.

• kino = the noun
• letní = an adjective describing kino

In Letní kino je dnes otevřené, the thing that is open is the summer cinema, so that noun phrase is the subject.

Je is the 3rd person singular form of být = to be.

So:

• je = is

Czech often uses být in sentences like this, just as English uses is:

• Kino je otevřené. = The cinema is open.

In some special styles, especially headlines or signs, Czech may omit je, but in a normal full sentence, je is standard.

Because it agrees with kino, which is a neuter singular noun.

Czech adjectives usually match the noun in:

• gender
• number
• case

Here:

• kino is neuter singular
• so otevřené is also neuter singular nominative

Compare:

• obchod je otevřený = the shop is open (masculine)
• restaurace je otevřená = the restaurant is open (feminine)
• kino je otevřené = the cinema is open (neuter)

Letní is the adjective formed from léto = summer.

It belongs to a group often called soft adjectives, which commonly end in -í in the dictionary form.

So:

• léto = summer
• letní = summer / summer-related

In this sentence, letní agrees with kino, but the nominative singular neuter form is still letní.

That may feel unusual if you are expecting endings like -ý, -á, -é, but letní follows a different adjective pattern.

Yes. That is also correct.

Both are natural:

• Letní kino je dnes otevřené.
• Letní kino je dnes otevřeno.

The difference is small:

• otevřené sounds more clearly like an adjective
• otevřeno can sound a bit more like a state or condition, and sometimes slightly more formal or notice-like

In everyday use, both can mean the same thing here.

Because Czech word order is fairly flexible, and this position is very natural and neutral.

The sentence structure is:

• Letní kino = subject
• je = is
• dnes = today
• otevřené = open

You can change the order to shift emphasis. For example:

• Letní kino je dnes otevřené. = neutral
• Dnes je letní kino otevřené. = emphasis on today
• Otevřené je dnes letní kino. = marked, less neutral

So the original word order is probably the most ordinary one.

Because Czech does not have articles like English a and the.

So letní kino can mean:

• a summer cinema
• the summer cinema

The exact meaning depends on context.

In this sentence, English would often use the if both speakers know which cinema is being discussed, but Czech simply leaves that to context.

In this sentence, dnes means today.

Czech dnes most commonly refers to the current day. In some contexts it can be used in a broader sense like these days / nowadays, but that is not the natural reading here.

So here the sentence is understood as saying that the summer cinema is open on this particular day.

Yes, kino is a neuter noun.

One clue is that many Czech neuter nouns in the singular end in:

• -o
• -e
• -í

Since kino ends in -o, it is typically neuter. That is why the adjective is:

• otevřené and not otevřený or otevřená

So the agreement in the sentence confirms the gender:

• to kino
• letní kino
• kino je otevřené

Not by itself. The sentence simply says that it is open today.

It does not automatically imply:

• that it was closed yesterday
• that it will be closed tomorrow
• that today is the only open day

If you wanted to say only today, Czech would use something extra, for example jen dnes or pouze dnes.