O segundo tempo começou rápido.

Yes, tempo often means time, but in sports Portuguese it can also mean a period of play.

In Brazilian soccer language:

• primeiro tempo = first half
• segundo tempo = second half

So here tempo is a sports term, not clock time in the general sense.

Because tempo is a masculine noun.

In Portuguese, the article and the ordinal have to agree with the noun:

• o segundo tempo
• not a segunda tempo

If the noun were feminine, you would use a segunda:

• a segunda etapa

Because in this sentence o segundo tempo is the subject of the verb.

The structure is:

• O segundo tempo = the second half
• começou = started
• rápido = quickly / fast

So the sentence means that the second half itself started fast.

If you said no segundo tempo, that would mean in the second half, which is a different structure:

• No segundo tempo, o time melhorou. = In the second half, the team improved.

Not in this sentence.

Segundo can mean:

• second when it is an ordinal number
• according to when it is used as a preposition

Compare:

• o segundo tempo = the second half
• segundo o técnico = according to the coach

Here, segundo is clearly the ordinal adjective modifying tempo.

Começou is the preterite form of começar for he/she/it:

• começar = to begin, to start
• começou = began, started

It is used because the sentence refers to a completed event in the past: the second half started.

Also, the subject is singular:

• o segundo tempo = it

So começou matches that singular subject.

Because Brazilian Portuguese often uses adjectives in an adverb-like way, especially in everyday speech and sports language.

So:

• começou rápido = started fast / started quickly

A more formally adverbial version would be:

• começou rapidamente

Both are understandable, but rápido sounds very natural and common in speech, commentary, and journalism.

In this sentence, it is functioning adverbially.

It is describing how the action started, not literally describing the second half as a noun.

So the idea is:

• It started fast not
• It was a fast second half as a noun description

This kind of usage is very common in Brazilian Portuguese:

• Ele fala baixo.
• Ela dirige rápido.
• O jogo começou forte.

Usually, no.

In a sports context, começou rápido normally means that the play started at a fast pace right away. It suggests intensity, speed, or quick action after the restart.

It usually does not mean that halftime itself was short.

If you wanted to talk about the break being short, you would normally say that more explicitly.

Yes, that is possible.

Portuguese word order is fairly flexible. These are both possible:

• O segundo tempo começou rápido.
• Começou rápido o segundo tempo.

The version with the subject first is more neutral and straightforward.

The version with the verb first can sound more like:

• narration
• sports commentary
• a more dramatic or lively style

Começou is pronounced with the stress on the last syllable:

• co-me-ÇOU

The ç is called cedilha, and it makes the c sound like s before a, o, or u.

So in começou, the ç sounds like s.

Without the cedilla, the c before o would normally sound like k, which would be wrong here.