Recyklace je pro naši domácnost důležitá.

Because pro takes the accusative case, and domácnost is a feminine singular noun.

So:

• naše domácnost = our household (nominative)
• pro naši domácnost = for our household (accusative)

The possessive pronoun náš / naše has to match the noun in gender, number, and case. Here it matches domácnost, so we get naši.

It is in the accusative singular.

That is because it follows the preposition pro, which requires the accusative:

• pro naši domácnost = for our household

The noun domácnost looks the same in nominative and accusative, but the pronoun before it changes, which helps show the case.

Because it agrees with recyklace, which is a feminine singular noun.

In Czech, predicate adjectives after je still agree with the subject:

• Recyklace je důležitá.
• Vzdělání je důležité.
• Sport je důležitý.

So:

• recyklace = feminine
• therefore důležitá = feminine singular

It is in the nominative, because it is the subject of the sentence.

The sentence structure is:

• Recyklace = subject
• je = is
• pro naši domácnost = for our household
• důležitá = important

So recyklace is the thing being described as important.

In normal standard Czech, je is needed here.

Czech uses the verb být (to be) in the present tense:

• Recyklace je důležitá. = Recycling is important.

Unlike in some other Slavic languages, standard Czech normally does not leave out is/are in regular sentences like this.

You might sometimes see omission in headlines, notes, or very compressed style, but not in ordinary full sentences.

Here pro means for.

So:

• pro naši domácnost = for our household

It shows who something matters to or who it is relevant for.

In this sentence, the idea is that recycling is important for our household / from the point of view of our household.

Yes, but the meaning changes slightly.

• Recyklace je pro naši domácnost důležitá.
  = Recycling is important for our household.

• Recyklace je v naší domácnosti důležitá.
  = Recycling is important in our household.

The first focuses more on relevance or benefit to the household.
The second focuses more on the setting: within our household, recycling is important.

Both can be natural, but they are not exactly identical.

Not exactly.

Domácnost usually means household: the people living together and their shared home life, budget, chores, etc.

Compare:

• dům = house/building
• byt = apartment/flat
• domov = home in a more emotional sense
• domácnost = household

So in this sentence, domácnost is a very good choice because recycling is something connected with how a household functions.

Because Czech does not have articles like English the and a/an.

So recyklace can mean:

• recycling
• the recycling
• sometimes even recycling in general

The exact meaning depends on context.

In this sentence, it is understood as a general statement about recycling.

It is a normal Czech word, although it is an international/borrowed-type word, like many words related to technology or environmental topics.

It behaves like a regular Czech noun:

• recyklace
• bez recyklace
• k recyklaci
• etc.

So even though it may look familiar to an English speaker, it still follows Czech grammar.

Yes. Czech word order is fairly flexible, because case endings show the grammatical relationships.

The neutral version is:

• Recyklace je pro naši domácnost důležitá.

But you could also say:

• Pro naši domácnost je recyklace důležitá.

This puts more emphasis on for our household.

You might also hear:

• Důležitá je pro naši domácnost recyklace.

That sounds more marked or stylistic, with stronger emphasis.

So the original sentence is a natural, neutral order.

A simple approximate pronunciation is:

RET-si-kla-tse ye pro NA-shi do-MAH-tsnost DOO-le-zhi-tah

A few helpful notes:

• ř is not in this sentence, so that is one less worry.
• c in recyklace is pronounced like ts
• je sounds roughly like ye
• š sounds like sh
• č is not present here
• stress in Czech usually falls on the first syllable of each word:
  • REcyklace
  • DOmácnost
  • DŮležitá

Usually it means recycling in general.

A bare singular noun in Czech often expresses a general concept:

• Recyklace je důležitá. = Recycling is important.

So this sentence most naturally means that recycling, as a practice, is important for the household.

If you wanted to refer to some specific recycling process or event, the context would usually make that clear.

Because domácnost here is the singular form.

Compare:

• domácnost = household
• domácnosti = households / households' / about the household, depending on case

So:

• pro naši domácnost = for our household
• pro naše domácnosti = for our households

The sentence clearly uses singular.

No. The structure is very reusable.

You can replace důležitá with many other feminine singular adjectives to match recyklace:

• Recyklace je pro naši domácnost užitečná. = Recycling is useful for our household.
• Recyklace je pro naši domácnost potřebná. = Recycling is necessary for our household.
• Recyklace je pro naši domácnost výhodná. = Recycling is beneficial for our household.

The important thing is that the adjective must stay feminine singular because of recyklace.

Sometimes yes, but the nuance is slightly different.

• recyklace = recycling as a concept/system/process
• recyklování = the act of recycling

In many contexts they are close, but recyklace sounds very natural in a general statement like this:

• Recyklace je pro naši domácnost důležitá.

Using recyklování would focus a bit more on the activity itself.