Politika této země je důležitá.

Politika can mean politics in a general sense, and in some contexts it can also mean policy.

In this sentence, the most natural meaning is usually the politics of this country is important or this country's politics is important.

A few useful notes:

• politika = politics / policy
• meaning depends on context
• it is a feminine noun

So the sentence is not about a single politician; it is about the political sphere or political affairs of the country.

Because země is not the subject here. It depends on politika.

The structure is:

• politika = the politics
• této země = of this country

In Czech, possession or a relationship like of this country is often expressed with the genitive case.

So:

• tato země = this country (nominative)
• této země = of this country (genitive)

That is why tato changes to této.

Země is in the genitive singular.

Why? Because after a noun like politika, Czech often uses the genitive to express of ...

So:

• politika země = the politics of the country
• politika této země = the politics of this country

This is a very common Czech pattern:

• hlavní město země = the capital of the country
• historie Evropy = the history of Europe
• prezident republiky = the president of the republic

Because důležitá agrees with politika.

In Czech, adjectives must agree with the noun they describe in:

• gender
• number
• case

Here:

• politika is feminine
• singular
• nominative (because it is the subject)

So the adjective must also be feminine singular nominative:

• masculine: důležitý
• feminine: důležitá
• neuter: důležité

That is why the sentence has důležitá, not důležitý or důležité.

Here je means is, and it is normally required.

The sentence pattern is:

• Politika této země = subject
• je = is
• důležitá = important

So literally:

• Politika této země je důležitá.
• The politics of this country is important.

Unlike in some languages, standard Czech usually does not omit the present-tense form of to be in sentences like this.

So you generally need je here.

Yes. The whole noun phrase Politika této země is the subject.

The core subject noun is politika.
The words této země just specify which politics:

• politika = politics
• této země = of this country

Then the predicate is:

• je důležitá = is important

So the sentence breaks down like this:

• Politika této země — subject
• je důležitá — predicate

Yes. Czech word order is more flexible than English, although the basic order here is very natural.

The neutral version is:

• Politika této země je důležitá.

You could also say:

• Důležitá je politika této země.
• Této země politika je důležitá. (possible, but less neutral and more marked/stylistic)

Changing the word order usually changes:

• emphasis
• topic/focus
• style

For a learner, the original order is the safest and most natural.

Because Czech has no articles like English a/an/the.

So Czech often expresses definiteness through:

• context
• word order
• demonstratives like ten, tato, tento
• general meaning

In this sentence, English needs the or another determiner:

• The politics of this country is important
• This country's politics is important

But Czech simply says:

• Politika této země je důležitá.

No article is needed.

Této is a form of the demonstrative this.

Its basic dictionary forms are:

• masculine: ten
• feminine: ta
• neuter: to

But when declined, the forms change.

Here této is the feminine singular genitive/dative/locative form, agreeing with země.

So:

• ta země = that/this country (basic feminine form with a demonstrative)
• této země = of this country

In other words, této matches the case and gender of země.

Yes, often you can.

• této země is more standard/written/formal-neutral
• téhle země is common in spoken Czech and more colloquial

So both can mean:

• of this country

Compare:

• Politika této země je důležitá. — neutral, standard
• Politika téhle země je důležitá. — more conversational

For learners, této is a very good form to know because it fits standard Czech well.

A rough pronunciation guide:

• této ≈ TAY-toh
• země ≈ ZEH-mnyeh
• je ≈ yeh
• důležitá ≈ doo-LEH-zhi-taa

A few key points:

• Czech stress is usually on the first syllable:
  • TÉ-to
  • ZE-mě
  • DŮ-le-ži-tá
• j is pronounced like English y in yes
• ž sounds like the s in measure
• ě often softens the preceding consonant, which is why země does not sound like simple ze-me

You do not need to pronounce it exactly like the rough English guide, but it can help at first.

Because some Czech nouns have the same form in more than one case.

For země, the form země can be:

• nominative singular: země = country / land
• genitive singular: země = of the country / of the land

So the noun itself does not visibly change here, but the demonstrative does:

• nominative: tato země
• genitive: této země

That is one clue showing the case.

Yes, absolutely.

That is often a very natural English translation.

Czech uses the structure:

• politika této země = literally the politics of this country

But in English, we often prefer the possessive form:

• this country's politics is important

So both translations are fine, depending on what sounds most natural in context.