Tento zákon je důležitý.

Both are possible, but they are not exactly the same.

• tento zákon = this law (more explicit, more specific)
• ten zákon = often that law, but in everyday Czech it can also sometimes mean this/the law depending on context

For a learner, the safest match is:

• tento = this
• ten = that

So Tento zákon je důležitý is a very clear way to say This law is important.

It is in the nominative singular.

Why? Because zákon is the subject of the sentence:

• Tento zákon = the thing being talked about
• je důležitý = is important

In Czech, the subject is normally in the nominative case.

Because it has to agree with zákon.

Zákon is:

• masculine
• singular
• nominative
• inanimate

The demonstrative tento changes its form to match the noun. For masculine singular nominative, the form is tento.

So:

• tento zákon = this law
• tato kniha = this book
• toto město = this city

This matching is called agreement.

For the same reason: it agrees with zákon.

Since zákon is masculine singular nominative, the adjective also takes the masculine singular nominative form:

• důležitý zákon = an important law
• zákon je důležitý = the law is important

So -ý here tells you the adjective is masculine singular nominative.

In this sentence, it comes after the verb because it is part of the predicate:

• Tento zákon je důležitý = This law is important

Here, důležitý means important as a description linked by je = is.

But adjectives can also go directly before the noun:

• důležitý zákon = an important law

So compare:

• důležitý zákon = a noun phrase
• zákon je důležitý = a full sentence

Je is the 3rd person singular present tense of být = to be.

So:

• je = is

In this sentence:

• Tento zákon je důležitý
• This law is important

Unlike in some other Slavic languages, Czech normally does use the present tense of to be in sentences like this.

Normally, no—not in a standard full sentence like this.

You usually need je:

• Tento zákon je důležitý = correct

Without it:

• Tento zákon důležitý = not a normal complete standard sentence

You might see the verb omitted in headlines, notes, or very informal speech, but for normal grammar, keep je.

No, Czech word order is fairly flexible, but changing it changes the emphasis.

The neutral order is:

• Tento zákon je důležitý.

Other orders are possible, for example:

• Důležitý je tento zákon. = It is this law that is important.
• Je tento zákon důležitý? = Is this law important?

So the basic meaning can stay similar, but the focus or style changes.

A rough guide is:

• dů- sounds like doo-
• -le- like leh
• -ži- has ž, which sounds like the s in measure
• -tý has a long ee-like vowel at the end

So approximately: doo-leh-zhi-tee

A few useful pronunciation points:

• ů is pronounced like a long ú
• ž sounds like the s in vision or measure
• ý is a long vowel

The difference is the demonstrative tento.

• Tento zákon je důležitý = This law is important
• Zákon je důležitý = The law is important or A law is important, depending on context

Czech has no articles like the or a, so words like tento help make the reference more specific.

Usually, yes—especially in the sense of a law, act, statute, or legal rule.

So in this sentence, zákon is most naturally understood as a legal law:

• Tento zákon je důležitý = This law is important

In other contexts, Czech can use different words for things like a scientific law or a general rule, depending on the meaning.

It is masculine inanimate, and yes, that matters.

Czech masculine nouns are split into:

• masculine animate
• masculine inanimate

Zákon is inanimate because it is a thing, not a person or animal.

This matters because adjectives, pronouns, and some case endings change differently for animate and inanimate masculine nouns. In the nominative singular, the form here is:

• tento zákon
• důležitý

That fits masculine inanimate singular.

Yes. Tenhle zákon je důležitý is a common everyday Czech way to say This law is important.

Compare:

• tento zákon = more neutral, standard, sometimes slightly more formal
• tenhle zákon = very common in spoken Czech, more conversational

So both are correct, but tento zákon is a good textbook-style form.