Současný zákon je důležitý.

Because they are adjectives agreeing with zákon.

Zákon is:

• masculine
• singular
• nominative

In Czech, adjectives must match the noun they describe in gender, number, and case.

So:

• současný zákon = current law
• zákon je důležitý = the law is important

If the noun changed, the adjective endings would change too:

• současná smlouva je důležitá = the current contract is important
• současné pravidlo je důležité = the current rule is important

It is in the nominative case.

That is because zákon is the subject of the sentence:

• Současný zákon = the subject
• je = is
• důležitý = predicate adjective describing the subject

In simple equational sentences like this, the subject is normally in the nominative.

Here, je is the 3rd person singular of být (to be), and it is normally required.

So:

• Současný zákon je důležitý. = correct
• Současný zákon důležitý. = not standard Czech

Unlike some languages, Czech usually does not drop the present-tense form of to be in normal declarative sentences.

Současný usually means:

• current
• present-day
• contemporary

In this sentence, současný zákon most naturally means the current law or the law currently in force.

Depending on context, it can also mean modern-day or present rather than former or historical.

Yes, there can be small differences in nuance.

• současný = current, present-day, contemporary
  Often fairly neutral and common.

• aktuální = current, topical, up-to-date
  Often suggests something very current, relevant right now, or topical.

• nynější = present, current
  A bit more literary or formal in some contexts.

So současný zákon sounds very natural for the current law.

Because Czech has no articles like a or the.

So zákon can mean:

• a law
• the law

The exact meaning depends on context.

In this sentence, English might translate it as The current law is important or A current law is important, but Czech does not mark that difference with an article.

Yes. Czech word order is fairly flexible, though the neutral order here is:

• Současný zákon je důležitý.

Other orders are possible, but they change emphasis:

• Je současný zákon důležitý? = Is the current law important?
  This is a question.

• Důležitý je současný zákon.
  This emphasizes important or contrasts the current law with something else.

• Současný zákon důležitý je.
  This can sound emphatic, like The current law is important indeed / is important, actually.

So the original sentence is the most neutral statement.

A few useful points:

• Czech stress is almost always on the first syllable of the word.
• ou in současný is a real diphthong, roughly like oh-oo said quickly.
• č sounds like ch in church.
• ž sounds like the s in measure.
• ů is pronounced like a long ú sound.
• ý is a long ee-like vowel, though not exactly the same as English ee.

A rough English-style approximation:

• současný ≈ SOU-cha-snee
• důležitý ≈ DOO-le-zhi-tee

Not perfect, but helpful as a starting point.

In modern Czech pronunciation, ú and ů are pronounced the same: a long u sound.

The difference is mostly historical and spelling-based.

A simple learner rule:

• ú usually appears at the beginning of a word or word part
• ů usually appears inside a word

So:

• úkol
• dům
• důležitý

You do not need to pronounce them differently.

Zákon is masculine inanimate.

That matters in Czech grammar, especially in some cases such as the accusative.
In this sentence, however, you only need to know that it is masculine singular nominative, which gives the adjective ending -ý.

Here:

• současný zákon
• důležitý

Both adjectives match a masculine singular noun.

Yes, it is perfectly natural Czech.

It is a neutral, standard sentence that could easily appear in:

• legal discussion
• news
• formal writing
• everyday conversation about rules or legislation

It sounds a bit formal mainly because zákon itself is a formal-ish noun, but grammatically and stylistically the sentence is completely normal.

The main change would be the adjective endings.

For example:

• Současný zákon je důležitý.
  masculine singular

• Současná pravidla jsou důležitá.
  plural neuter noun pravidla → adjective and verb change

• Současná smlouva je důležitá.
  feminine singular

• Současné nařízení je důležité.
  neuter singular

This is a very important Czech pattern: adjectives must agree with the noun, and the verb must agree with the subject in number.