Naše domácnost je malá.

Because naše has to agree with domácnost.

In Czech, possessive words like my / our change form depending on the noun they describe. Domácnost is:

• feminine
• singular
• nominative here

So the correct form is naše.

A few related forms:

• náš dům = our house
• naše domácnost = our household
• naše auto = our car

So náš is not the basic form you always use for our; it changes to match the noun.

Domácnost usually means household rather than the physical building itself.

It can refer to:

• the people living together as one household
• the running of a home
• a household as a social or economic unit

So Naše domácnost je malá most naturally means Our household is small.

It is not usually the best word if you specifically mean:

• house/building = dům
• home in an emotional sense = domov
• flat/apartment = byt

Because the adjective has to agree with domácnost.

Since domácnost is feminine singular, the adjective also takes the feminine singular nominative form:

• malý = masculine
• malá = feminine
• malé = neuter

So:

• malý dům = a small house
• malá domácnost = a small household
• malé auto = a small car

This kind of adjective agreement is a basic feature of Czech grammar.

Je means is. It is the 3rd person singular form of the verb být = to be.

So the sentence structure is:

• Naše domácnost = subject
• je = is
• malá = complement/adjective

Unlike in some languages, Czech normally uses the present-tense form of to be in sentences like this:

• Dům je velký. = The house is big.
• Město je krásné. = The city is beautiful.

In very informal speech, people may sometimes leave out je, but for standard Czech, keeping it is correct.

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

So domácnost can mean:

• a household
• the household
• just household

The exact meaning depends on context.

In this sentence, naše already makes the noun specific, so English naturally uses our household.

Not completely. Czech word order is more flexible than English because endings carry a lot of grammatical information.

The neutral order here is:

• Naše domácnost je malá.

But other orders are possible for emphasis, for example:

• Malá je naše domácnost.
• Naše domácnost malá je. (more marked or poetic)

These versions do not usually change the basic meaning, but they change the focus or emphasis. For learners, the original order is the safest and most natural one.

A rough pronunciation guide for an English speaker is:

NAH-sheh doh-MAAH-tsnost yeh mah-LAA

A few sound notes:

• š sounds like sh in ship
• á is a long vowel, so hold it slightly longer
• je sounds like ye
• c in domácnost sounds like ts

So:

• Naše ≈ NAH-sheh
• domácnost ≈ doh-MAAH-tsnost
• je ≈ ye
• malá ≈ mah-LAA

It is singular here.

You can tell from:

• naše domácnost = singular noun
• je = is (singular verb)
• malá = feminine singular adjective

The plural would be:

• domácnosti = households
• Naše domácnosti jsou malé. = Our households are small.

Not in this sentence.

Here naše is being used before a noun, so it means our:

• naše domácnost = our household

If you want ours as a standalone pronoun, Czech often uses different structures depending on context, for example:

• To je naše. = That is ours.

So in your sentence, naše is definitely the possessive adjective-like form meaning our.

Sometimes yes, but it depends on what you want to express.

• domácnost = household
• domov = home in the sense of belonging
• dům = house

So:

• Naše domácnost je malá. = Our household is small.
• Náš domov je malý. = Our home is small.
• Náš dům je malý. = Our house is small.

English sometimes uses home more loosely, but if you are learning vocabulary precisely, household is the best match for domácnost.

You usually learn the gender with the noun, because it affects lots of other words in the sentence.

In this sentence, you can see it is feminine because:

• the possessive form is naše
• the adjective form is malá

Also, many Czech nouns ending in -ost are feminine, including:

• radost = joy
• rychlost = speed
• společnost = company/society
• domácnost = household

This is a useful pattern, though as always, learners should still memorize gender with each noun.