A polícia vai investigar o problema.

A is the feminine singular definite article, meaning the.

So:

• a polícia = the police

In Portuguese, nouns usually need an article more often than in English. Here, polícia is a feminine noun, so it takes a, not o.

No. The gender here is grammatical gender, not biological sex.

Polícia is a feminine noun, so Portuguese uses:

• a polícia
• a polícia vai investigar

That does not mean the officers are women. It just means the noun itself is feminine.

In this sentence, a polícia means the police as a force or institution.

That is why the verb is singular:

• A polícia vai investigar...

Portuguese often treats polícia as a singular collective noun here, even though English uses a plural-looking idea: the police.

So this sentence is not normally understood as the policewoman is going to investigate the problem.

Because a polícia is grammatically singular in this sentence.

• a polícia = singular
• vai = third person singular of ir

So Portuguese matches the verb to the grammatical form of the subject:

• A polícia vai investigar...

Even though English says the police are/will, Portuguese often uses singular agreement with a polícia when referring to the institution.

Vai investigar is the very common ir + infinitive future structure.

It is built like this:

• vai = goes / is going
• investigar = to investigate

Together, vai investigar means:

• is going to investigate
• often simply will investigate

In everyday Portuguese, this structure is extremely common and natural.

Yes. You could also say:

• A polícia investigará o problema.

That also means The police will investigate the problem.

The difference is mainly one of style:

• vai investigar = more common in everyday speech
• investigará = more formal, more written, sometimes less conversational

Because o problema refers to a specific problem, not just the idea of a problem in general.

• o = the
• o problema = the problem

Portuguese uses definite articles very naturally in cases where English would also usually use the.

Because not all nouns ending in -a are feminine.

Problema is a masculine noun:

• o problema
• um problema

This is a common pattern with some words of Greek origin ending in -ma, such as:

• o problema
• o sistema
• o tema
• o programa

So the ending -a does not always mean the noun is feminine.

No. Investigar normally takes a direct object, just like English to investigate.

So you say:

• investigar o problema = to investigate the problem

Not:

• investigar sobre o problema for this basic meaning

The simplest and most natural structure here is:

• A polícia vai investigar o problema.

No. This is the normal basic word order in Portuguese:

• Subject + verb + object

So:

• A polícia = subject
• vai investigar = verb phrase
• o problema = object

It is a very standard sentence structure and a good pattern to copy.

The stress is on -cí-:

• po-LÍ-ci-a

In European Portuguese, the unstressed vowels are reduced, so it sounds roughly like:

• puh-LEE-see-uh
  or more tightly in fast speech.

The written accent in polícia shows where the stress goes.

Yes. In many contexts, both translations work.

So this sentence can be understood as:

• The police are going to investigate the problem
• The police will investigate the problem

The Portuguese structure ir + infinitive often overlaps with English future meaning very naturally.