Část nábytku je zničená.

Because část usually takes the genitive case in Czech.

So the structure is:

• část = part
• nábytku = of the furniture

The basic dictionary form is nábytek, but after část, it changes to the genitive singular: nábytku.

This is very common in Czech with words meaning quantity or portion, for example:

• kus chleba = a piece of bread
• sklenice vody = a glass of water
• část města = part of the city

So část nábytku literally works like part of the furniture.

Because the adjective agrees with část, not with nábytku.

The subject of the sentence is část and část is a feminine noun. In Czech, adjectives and past/passive-type forms agree with the noun they describe in:

• gender
• number
• case

So:

• část = feminine singular
• therefore zničená = feminine singular

Even though nábytku is masculine, it is only part of the genitive phrase část nábytku. The main noun is still část.

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

So:

• Část nábytku je zničená.
• literally: Part of the furniture is destroyed/damaged.

In Czech, when you make this kind of present-tense statement with an adjective or adjective-like form, je is normally required.

Compare:

• Dům je velký. = The house is big.
• Místnost je čistá. = The room is clean.
• Část nábytku je zničená. = Part of the furniture is damaged.

It is related to the verb zničit = to destroy.

Zničený / zničená / zničené behaves like an adjective and means:

• destroyed
• ruined
• badly damaged

It agrees like a normal adjective:

• zničený stůl = a destroyed table
• zničená židle = a destroyed chair
• zničené auto = a destroyed car

In this sentence, it works as a predicate adjective after je:

• je zničená = is destroyed / is damaged

Yes, Czech word order is flexible, but this version is the most neutral.

The neutral structure is:

• subject + je + description

So:

• Část nábytku = subject
• je zničená = what is being said about it

Other word orders are possible, but they change emphasis:

• Zničená je část nábytku. = It is part of the furniture that is damaged.
• Část nábytku zničená je. = possible, but marked or emphatic

For a learner, Část nábytku je zničená is the safest and most standard version.

Normally, no.

Since the subject is část, which is feminine singular, the agreeing form should be zničená.

So the correct sentence is:

• Část nábytku je zničená.

Using zničeno would not agree with část.
Zničeno is neuter singular or can be used in impersonal/passive-style expressions, such as:

• Je zničeno mnoho domů. = Many houses have been destroyed.

But in your sentence, where the subject is clearly část, agreement with část is expected.

Nábytek is a singular mass noun.

It works a lot like furniture in English:

• English: furniture is grammatically singular, even though it refers to many items
• Czech: nábytek is also grammatically singular

So:

• ten nábytek = that furniture
• nový nábytek = new furniture

In your sentence, nábytku is still singular, just in the genitive case.

Because část is the subject here, so it is in the nominative singular: část.

The form části could be something else depending on context, for example:

• genitive singular
• dative singular
• locative singular
• nominative plural / accusative plural in some contexts

But in this sentence, you need the basic subject form:

• část = part

So:

• Část nábytku je zničená. = Part of the furniture is damaged.

Nábytek is masculine inanimate.

Its dictionary form is:

• nábytek = furniture

Some useful forms:

• nominative singular: nábytek
• genitive singular: nábytku

Even though it is masculine, that does not control the form zničená here, because the adjective agrees with část, not with nábytek.

Yes. In real usage, zničený / zničená / zničené can cover a range from ruined or wrecked to simply badly damaged, depending on context.

So this sentence could sound like:

• part of the furniture is destroyed
• part of the furniture is ruined
• part of the furniture is damaged

If the context is less extreme, Czech might also use words like:

• poškozená = damaged
• rozbitá = broken

But zničená is a perfectly natural choice if the furniture is in very bad condition.

A rough English-friendly guide would be:

• Část ≈ chaast
• nábytku ≈ NAA-bit-koo
• je ≈ ye
• zničená ≈ ZNEE-cheh-naa

A few useful pronunciation notes:

• Č sounds like ch in check
• á is a long vowel
• y in nábytku is not exactly English i, but learners often approximate it with a short i
• c in zničená is not present; the č again sounds like ch
• j in Czech is like English y in yes

So the whole sentence is approximately:

chaast NAA-bit-koo ye ZNEE-cheh-naa

Yes, but that changes the tense.

• je zničená = is destroyed / is damaged
• byla zničená = was destroyed / was damaged

So if you are talking about the present state, use:

• Část nábytku je zničená.

If you are talking about the past, use:

• Část nábytku byla zničená.

The pattern is:

[noun in nominative] + [genitive complement] + [form of být] + [adjective agreeing with the main noun]

In this sentence:

• Část = main noun, nominative singular, feminine
• nábytku = genitive singular, dependent on část
• je = is
• zničená = feminine singular adjective-like form agreeing with část

So the grammar is very systematic:

• část čeho? = part of what?
• nábytku = of the furniture

and then:

• část ... je zničená = the part ... is damaged/destroyed

That is why every piece of the sentence has the form it does.