Stavba nového domu začala.

Because stavba is in the nominative singular, which is the normal case for the subject of a sentence.

So the structure is:

• stavba = the subject
• začala = the verb, agreeing with the subject
• nového domu = a dependent phrase meaning of a new house

So grammatically, the sentence is built around stavba:
The construction of a new house started.

Because it agrees with stavba, and stavba is a feminine singular noun.

In the Czech past tense, the verb form changes to match the subject's gender and number:

• masculine singular: začal
• feminine singular: začala
• neuter singular: začalo
• plural: začali / začaly

Since stavba is feminine singular, the correct form is začala.

In Czech, the past tense is formed differently from English.

Here, začala by itself already means started / began. In the 3rd person Czech does not use an extra auxiliary like English does.

Compare:

• začal jsem = I started
• začal jsi = you started
• začala = she/it started

So in this sentence, začala is a complete past-tense verb form on its own.

Because they are not the subject. They depend on stavba and mean construction of a new house.

Czech often uses the genitive case after a noun to express of something.
So:

• stavba domu = construction of a house
• stavba nového domu = construction of a new house

That is why both words change form:

• nový → nového
• dům → domu

domu is genitive singular of dům.

It is genitive because stavba commonly takes a genitive complement:
stavba čeho? = construction of what?

So:

• dům = house (nominative)
• domu = of a house (genitive)

This is very common in Czech with nouns derived from actions or processes.

Because Czech adjectives must agree with the noun they describe in:

• gender
• number
• case

Here, nového describes domu, so it must match domu:

• dům = masculine inanimate singular
• domu = genitive singular
• therefore nový becomes nového

So the pair is:

• nový dům = a new house
• nového domu = of a new house

It can mean either, depending on context.

Common meanings of stavba include:

• the process of construction
• a structure/building

In this sentence, because of the verb začala (started / began), the process meaning is the natural one. A physical building usually does not start, but construction does.

So here stavba is best understood as construction or building work.

It is connected to stavba, not directly to the verb.

The phrase is:

• stavba nového domu = construction of a new house

Then the whole noun phrase is the subject of the sentence:

• Stavba nového domu = the construction of a new house
• začala = started

So the sentence is not saying that someone started a new house. It is saying that the construction of the new house began.

Yes. That would also be correct.

Czech word order is much more flexible than English word order. The choice often depends on emphasis, information structure, or style.

Both are possible:

• Stavba nového domu začala.
• Začala stavba nového domu.

A rough difference:

• Stavba nového domu začala. → focuses first on the construction
• Začala stavba nového domu. → sounds more like the construction of a new house has begun

Both are natural.

Because Czech has no articles.

Unlike English, Czech does not have separate words equivalent to a/an and the. Whether something is definite or indefinite is usually understood from:

• context
• word order
• general situation

So stavba nového domu can mean either:

• the construction of a new house
• construction of a new house

The exact English choice depends on context.

It comes from the verb začít = to begin / to start.

začít is a perfective verb. That means it presents the action as a complete event, here specifically the beginning itself.

So začala means that the beginning happened.

If you used the imperfective začínala, the meaning would be different, for example:

• stavba začínala = the construction was starting / used to start

In this sentence, začala is the normal choice because it reports a completed beginning.

In this case, yes: stavba is a feminine noun.

Many Czech nouns ending in -a are feminine, and stavba follows that pattern. That is why it takes feminine agreement:

• ta stavba
• stavba začala

It is a good rule of thumb, though like most Czech patterns, there are a few exceptions elsewhere in the language.