Tato informace je důležitá.

Because informace is a feminine singular noun, and the demonstrative this has to agree with it.

Czech this changes by gender:

• tento = masculine
• tato = feminine
• toto = neuter

So:

• tato informace = this information
• tento dokument = this document
• toto město = this town

The shorter form ten / ta / to usually means that, though in everyday speech it can sometimes overlap with this/that depending on context.

Tato is a demonstrative pronoun/determiner. In this sentence, it works like this in English and directly modifies the noun informace.

It must match the noun in:

• gender
• number
• case

Here it is:

• feminine
• singular
• nominative

because informace is the subject of the sentence.

Because důležitá is an adjective, and it must agree with informace.

Since informace is:

• feminine
• singular
• nominative

the adjective also takes the feminine singular nominative ending -á.

Compare:

• důležitý dokument = important document (masculine)
• důležitá informace = important information (feminine)
• důležité město = important town/city (neuter)

So the ending is not random; it shows grammatical agreement.

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

In Tato informace je důležitá, the thing being described is informace, so it appears in nominative.

The adjective and demonstrative match that:

• tato = feminine singular nominative
• informace = nominative singular
• důležitá = feminine singular nominative

Here je is the normal present-tense form of být (to be), meaning is.

So the structure is:

• Tato informace = subject
• je = is
• důležitá = important

In standard full sentences, je is perfectly normal and expected.

Czech can sometimes omit forms of to be in:

• headlines
• notes
• very compressed styles
• some colloquial expressions

But in an ordinary sentence like this, je is the standard choice.

Yes. Tahle informace je důležitá is very common in everyday spoken Czech.

The difference is mainly style:

• tato informace = more neutral, standard, slightly more formal or written
• tahle informace = more colloquial, everyday spoken Czech

Both mean basically the same thing.

Yes. Czech word order is more flexible than English word order because endings show grammatical relationships.

The neutral order here is:

• Tato informace je důležitá.

But other orders are possible for emphasis, for example:

• Důležitá je tato informace. = It is this information that is important.
• Tato informace důležitá je. = possible, but marked/emphatic

So while the original sentence is the most natural neutral version, other orders can be used to shift focus.

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

So a noun like informace can mean:

• information
• the information
• in some contexts something close to an item of information

The exact meaning comes from context, word order, and demonstratives like tato.

Here, tato already makes it specific, so tato informace clearly means this information.

In this sentence it is singular.

You can tell from tato, which is feminine singular nominative. If it were plural, you would expect:

• tyto informace = these pieces of information / these items of information

So:

• tato informace je důležitá = this information is important
• tyto informace jsou důležité = these pieces of information are important

This can be confusing because some Czech noun forms look the same in singular and plural, but agreement usually makes it clear.

A simple pronunciation guide is:

• dů sounds roughly like doo
• le like leh
• ži like zhi in measure
• tá like taa, with a long a

So approximately: doo-leh-zhi-taa

A few useful points:

• ů is pronounced like a long ú sound, basically oo
• ž sounds like the s in measure
• á is a long vowel

The stress in Czech is normally on the first syllable:

• DŮ-le-ži-tá

Yes, and that is also very natural, but the structure is slightly different.

• Tato informace je důležitá. = This information is important.
• Tohle je důležitá informace. = This is important information.

The first sentence directly identifies this information as the subject. The second starts with this as a stand-alone pronoun (tohle) and then says what it is.

Both are correct, but they are not exactly the same grammatical structure.