A corrida melhora a saúde.

Because corrida here is a specific noun phrase with the definite article a, meaning running in a general, abstract sense.

In Portuguese, it is very common to use the definite article with general nouns, much more often than in English. So:

• A corrida melhora a saúde. = Running improves health.

Even though English usually leaves out the here, Portuguese often keeps it.

Here, corrida means running as an activity or form of exercise.

It comes from the verb correr (to run), but in this sentence it is a noun, not a verb.

Compare:

• Eu corro todos os dias. = I run every day.
• A corrida faz bem. = Running is good for you.

So corrida is like running or the practice of running.

Because the subject is a corrida, which is singular.

In Portuguese, the verb has to agree with the subject:

• A corrida melhora a saúde. = singular subject, singular verb
• As corridas melhoram a saúde. = plural subject, plural verb

So melhora is the third person singular form of melhorar.

Here, melhora is a verb: improves.

That can be confusing because melhora can also be a noun in other contexts, meaning improvement.

In this sentence:

• A corrida melhora a saúde.
  = Running improves health.

So it is functioning as the verb from melhorar (to improve).

For the same reason as with a corrida: Portuguese often uses the definite article with nouns in a general sense.

So:

• a saúde = health

Even though English usually says just health, Portuguese commonly says a saúde.

This is very natural in Brazilian Portuguese:

• A água faz bem para a saúde.
• O exercício melhora a saúde.

Yes. Corrida can mean:

• running as an activity
• race

The meaning depends on context.

Examples:

• A corrida melhora a saúde. = Running improves health.
• A corrida começa às 9h. = The race starts at 9.

So in your sentence, the health-related context makes running the natural meaning.

Because Portuguese usually prefers a noun like corrida in this kind of sentence, rather than the infinitive correr.

While Portuguese can sometimes use the infinitive as a subject, a corrida sounds more natural and standard here for running as an activity.

So:

• A corrida melhora a saúde. = very natural
• Correr melhora a saúde. = possible in some contexts, but less neutral and less likely as a basic textbook sentence

A simple approximate pronunciation is:

ah koh-HEE-dah meh-LYOH-rah ah sah-OO-jee

A few notes:

• rr in corrida is a stronger guttural h-like sound in Brazilian Portuguese.
• lh in melhora sounds like ly in million, but smoother.
• d before e/i in many Brazilian accents sounds like j, so saúde often sounds like sah-OO-jee.

The base form is melhorar, which means to improve.

Here is the relevant conjugation:

• eu melhoro = I improve
• você/ele/ela melhora = you/he/she improves

So in A corrida melhora a saúde, melhora matches the singular subject a corrida.

Yes, you could, but the meaning changes slightly.

• A corrida melhora a saúde. = Running improves health in a general sense.
• A corrida melhora sua saúde. = Running improves your health.

So a saúde is more general, while sua saúde makes it personal or directed toward someone.

The normal and most natural order is:

• A corrida melhora a saúde.

Portuguese does allow some flexibility, but changing the order can sound marked, literary, or unnatural in a simple statement.

For a beginner, it is best to stick with:

subject + verb + object

• A corrida = subject
• melhora = verb
• a saúde = object

It would become:

• As corridas melhoram a saúde.

Changes:

• a → as
• corrida → corridas
• melhora → melhoram

But note that as corridas means the runs/races or running sessions, not the general activity in the same broad way. The singular a corrida is more natural for the general idea running.