Studium jazyka je důležité.

Because jazyka is the genitive singular form of jazyk.

In Czech, the noun studium often takes another noun in the genitive to mean study of .... So:

• jazyk = language
• jazyka = of a language

So the structure is literally something like study of a language.

A very similar pattern appears in other phrases too:

• studium literatury = study of literature
• studium historie = study of history

Jazyka is genitive singular.

Its dictionary form, or base form, is jazyk. That is the nominative singular form.

So the forms here are:

• jazyk = nominative singular
• jazyka = genitive singular

A native English speaker often asks this because English usually does not change nouns much, but Czech uses endings very heavily.

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

In this sentence:

• studium = neuter singular
• důležité = neuter singular adjective form

Czech adjectives must agree in gender, number, and often case with the noun they describe or with the subject in this kind of sentence.

Compare:

• jazyk je důležitý = the language is important
  (jazyk is masculine)
• kniha je důležitá = the book is important
  (kniha is feminine)
• studium je důležité = the study is important
  (studium is neuter)

Studium is neuter.

A useful clue is its ending: many Czech neuter nouns end in -um, -o, or -í. The ending -um is especially common in learned or international words such as:

• studium
• muzeum
• centrum

Because studium is neuter, the adjective becomes důležité.

In a normal present-tense sentence like this, je is normally required.

So:

• Studium jazyka je důležité. = correct standard sentence

Leaving out je would usually sound incomplete in ordinary Czech. You may sometimes see omission in headlines, notes, or very compressed style, but not as the normal full sentence.

So for learners, the safe rule is: in the present tense, keep je.

Because Czech has no articles.

English says things like a language or the language, but Czech usually does not have a separate word for that. The meaning comes from context.

So Studium jazyka je důležité could be understood in English as:

• The study of a language is important
• Language study is important
• Studying a language is important

The exact English article depends on context, not on a Czech word.

Yes. Czech word order is more flexible than English word order.

The basic version here is:

• Studium jazyka je důležité.

But you could also say:

• Důležité je studium jazyka.

Both are grammatical. The difference is mainly in emphasis and information structure.

Very roughly:

• Studium jazyka je důležité. = neutral statement
• Důležité je studium jazyka. = emphasizes important

So Czech word order is not random, but it is much freer than in English.

A simple learner-friendly guide is:

• Studium ≈ STU-di-um
• jazyka ≈ YA-zi-ka
• je ≈ ye
• důležité ≈ DOO-le-zhi-teh

A few important pronunciation points:

• Czech stress is usually on the first syllable of each word.
• j is pronounced like English y.
• ž is like the sound in measure.
• ů means a long u sound, roughly like oo in food, but held longer.
• é is also long.

So the stress pattern is roughly:

• STUdium
• YAzyka
• ye
• DOOležité

Yes. That is also a correct Czech sentence.

• Studium jazyka je důležité. = The study of a language is important / Language study is important
• Studovat jazyk je důležité. = To study a language is important / Studying a language is important

The difference is mostly stylistic:

• studium jazyka sounds a bit more noun-like and sometimes slightly more formal
• studovat jazyk uses an infinitive, which can feel more direct

Both are useful and natural.

It can mean both language and tongue.

Like English, Czech uses the same word for both ideas:

• jazyk = language
• jazyk = tongue

In this sentence, because it follows studium, it clearly means language, not the body part.

Context normally makes the meaning obvious.

Not exactly. Studium usually sounds a bit more like study, studies, or the process of studying, and it can sound somewhat formal or academic.

In this sentence, it works very well. But Czech also has other ways to express similar ideas, for example:

• učení se jazyku = learning a language
• studování jazyka = studying a language
• studovat jazyk = to study a language

So studium jazyka is natural, but it is not the only possible expression.

Because it is not an adverb here. It is an adjective used with je to describe the subject studium jazyka.

So the structure is:

• Studium jazyka = subject
• je = is
• důležité = important

If it were an adverb, it would describe a verb, not a noun or subject. But here important is a property of studium, so Czech uses the adjective form agreeing with the subject.