Rozhodnutí soudu je důležité.

It is nominative singular because it is the subject of the sentence — the thing that is important.

You can tell from the rest of the sentence:

• je is singular
• důležité is the neuter singular form

So the sentence is built around rozhodnutí as one singular subject.

Because it is genitive singular of soud.

In Czech, when one noun means of X, the second noun is often put in the genitive:

• rozhodnutí soudu = decision of the court

So soudu answers the question whose decision? or decision of what?

The form soudu can be genitive, dative, or locative singular, depending on context. But in this sentence it is understood as genitive because it depends directly on rozhodnutí:

• rozhodnutí soudu = the court’s decision

If you wanted to the court or for the court, that would be a different structure. For example:

• Rozhodnutí je soudu důležité.
  = The decision is important to the court.

So word order and structure matter a lot here.

Because rozhodnutí is a neuter noun, and adjectives in Czech must agree with the noun in gender and number.

So:

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

Here the subject is rozhodnutí, which is neuter singular, so the correct form is důležité.

Yes. Even when the adjective comes after je and works as a predicate adjective, it still agrees with the subject.

So in:

• Rozhodnutí soudu je důležité

the adjective důležité agrees with rozhodnutí.

This is similar to:

• Auto je nové.
• Kniha je nová.
• Dům je nový.

The adjective changes to match the subject.

Here je is the normal present-tense form of být = to be.

Czech usually does use the present tense of to be in sentences like this:

• To je pravda.
• Dům je velký.
• Rozhodnutí soudu je důležité.

So unlike some languages where the present-tense copula may be dropped, in standard Czech you normally keep je.

Potentially either, depending on context.

Czech has no articles like a or the, so the sentence itself does not mark definiteness the way English does. Context tells you whether the meaning is:

• the court’s decision
• a court’s decision
• the decision of the court

In many real contexts, English will naturally translate it as the court’s decision or the court decision / court ruling, but Czech leaves that open unless the situation makes it clear.

No. The given order is the most neutral one:

• Rozhodnutí soudu je důležité.

But Czech word order is flexible and can change for emphasis or style. For example:

• Důležité je rozhodnutí soudu.

This puts more emphasis on important.

Even when the order changes, the cases help show what belongs together:

• rozhodnutí = subject
• soudu = genitive dependent on rozhodnutí

Good question — rozhodnutí can indeed look the same in nominative singular and nominative plural.

Here it is singular because:

• the verb is je = singular
• the adjective is důležité = neuter singular

If it were plural, you would normally have:

• Rozhodnutí soudu jsou důležitá. = The court’s decisions are important.

So the agreement tells you the number.

A simple pronunciation guide is:

ROZ-hod-nu-tí SOU-du ye DŮ-le-ži-té

A few useful points:

• Czech stress is usually on the first syllable of each word.
• ou in soudu is a real diphthong.
• ž sounds like the s in measure.
• ů and í / é mark long vowels.

So the rhythm is fairly regular:

• ROZhodnutí
• SOUdu
• je
• DŮležité

Yes. Soudní rozhodnutí is also a natural expression and means something like court decision or judicial decision.

The difference is mainly structural:

• rozhodnutí soudu = decision of the court
• soudní rozhodnutí = court/judicial decision

Both are valid, but rozhodnutí soudu more clearly points to a specific court as the source of the decision.