Toto je státní škola.

Because toto here does not directly modify škola.

In Toto je státní škola, toto means this as a standalone pronoun: this thing / this here. Then státní škola identifies what it is: a state school.

So the structure is basically:

• toto = this
• je = is
• státní škola = state school

If you wanted to say this school, where this directly describes school, then the demonstrative must agree with škola and you would say:

• Tato škola... = this school...

Compare:

• Toto je státní škola. = This is a state school.
• Tato škola je státní. = This school is state-run / public.

Here is the breakdown:

• Toto = this
• je = is
• státní = state, state-run, public
• škola = school

So grammatically:

• toto is the subject-like demonstrative pronoun
• je is the 3rd person singular of být (to be)
• státní škola is the predicate noun phrase telling you what this is

The key forms here are in the nominative.

• toto is nominative neuter singular
• škola is nominative singular
• státní agrees with škola

This is normal after je when you are identifying something:

• To je škola. = That/This is a school.
• Toto je státní škola. = This is a state school.

In other words, Czech usually uses the nominative for this kind of X is Y sentence.

Because Czech has no articles.

English needs:

• a school
• the school

Czech simply says:

• škola

Whether it means a school, the school, or just school depends on context.

So Toto je státní škola can naturally correspond to This is a state school. In the right context, Czech still does not need an article.

Státní is an adjective, and it belongs to a type of Czech adjective that often has -í in the dictionary form.

It means state / state-run / governmental / public depending on context.

In this sentence, it agrees with škola, but the form státní stays the same here. You will also see:

• státní škola = state school
• státní podnik = state enterprise
• státní muzeum = state museum

So even though the noun changes gender, státní looks the same in nominative singular.

It can be, but you need to be careful with English varieties.

In Czech, státní škola means a school run by the state or public authorities. That usually matches:

• state school in British English
• public school in much of American English

But in British English, public school can mean a specific kind of expensive private school, which is not what Czech státní škola means.

So for learners, state school is often the safest direct equivalent.

Yes — and in everyday speech, To je státní škola is often more natural.

Very roughly:

• to = very common, neutral this/that/it
• toto = more explicit, sometimes more formal, literary, or emphatic
• tohle = common colloquial this here

So all of these are possible in the right context:

• To je státní škola.
• Tohle je státní škola.
• Toto je státní škola.

For normal conversation, many speakers would probably choose to or tohle more often than toto.

No, not in a normal standard sentence like this.

Czech does not usually omit the present tense of to be in this structure.

So you need:

• Toto je státní škola.

Not:

• Toto státní škola. ✗

A simple learner-friendly pronunciation is:

TOH-toh yeh STAAT-nee SHKOH-lah

A few useful points:

• Czech stress is usually on the first syllable of each word.
• á is a long a sound.
• š sounds like English sh.
• je sounds roughly like yeh.

So:

• toto ≈ TOH-toh
• je ≈ yeh
• státní ≈ STAA-tnee
• škola ≈ SHKOH-lah

Not completely. Czech word order is more flexible than English word order.

Toto je státní škola is a normal, neutral version.

But depending on emphasis, you may also hear things like:

• Je to státní škola. = It is a state school.
• Státní škola to je. = more marked, contrastive emphasis

Even when the order changes, the meaning often stays similar, while the focus or emphasis changes.

They are close, but not identical.

• Toto je státní škola. = This is a state school.
  You are identifying what something is.

• Tato škola je státní. = This school is state-run / public.
  You are talking about a specific school and describing it.

So the first sentence points to something and names it.
The second starts with this school as a known noun phrase and then gives information about it.