Depois que eu fritar o alho, vou cozinhar o arroz.

It looks like the infinitive, but here it is actually the future subjunctive.

With many regular verbs, the future subjunctive form is identical to the infinitive, so that can be confusing at first:

• infinitive: fritar
• future subjunctive: quando eu fritar, depois que eu fritar

In this sentence, it is not functioning as a dictionary form like to fry. It is a conjugated verb meaning something like when/after I fry.

Because the sentence is talking about a future action that has not happened yet.

Portuguese commonly uses the future subjunctive after time expressions such as:

• quando
• depois que
• assim que
• logo que

So:

• Depois que eu fritar o alho, vou cozinhar o arroz.

means the frying will happen first, and only after that will the rice be cooked.

This is a very normal pattern in Portuguese. English usually just uses the present tense in similar clauses, as in After I fry the garlic, I’ll cook the rice, but Portuguese often uses the future subjunctive instead.

Yes. That is also possible.

You have a few natural options:

• Depois que eu fritar o alho, vou cozinhar o arroz.
• Depois de eu fritar o alho, vou cozinhar o arroz.
• Depois de fritar o alho, vou cozinhar o arroz.

The last one is especially common when the subject is clearly the same person in both actions.

Very roughly:

• depois que + conjugated verb = very common, clear, explicit
• depois de + infinitive = also common, often a little more compact

In everyday Brazilian Portuguese, all of these can sound natural depending on style and context.

Yes, it can often be left out:

• Depois que eu fritar o alho, vou cozinhar o arroz.
• Depois que fritar o alho, vou cozinhar o arroz.

Portuguese often drops subject pronouns because the verb form usually shows the subject. However, in the future subjunctive, some forms are identical for different subjects:

• eu fritar
• você fritar
• ele/ela fritar

Because of that, adding eu can make the sentence clearer.

So eu is not strictly necessary here, but it is very natural and helpful.

Because ir + infinitive is the most common everyday way to talk about the future in Brazilian Portuguese.

So:

• vou cozinhar = I’m going to cook / I will cook

The simple future:

• cozinharei

is grammatically correct, but it often sounds more formal, literary, or less conversational in Brazil.

In normal speech, Brazilians usually prefer:

• vou cozinhar
• vou fazer
• vou sair

rather than:

• cozinharei
• farei
• sairei

Portuguese uses articles more often than English.

In cooking contexts, o alho and o arroz can refer to the ingredient in a general but contextually understood way:

• fritar o alho
• cozinhar o arroz

This sounds very natural in Portuguese, even where English would often omit the article.

Without the article, the phrase may sound less natural or more specialized depending on the context. In ordinary cooking instructions, using the article is usually the safest choice.

Yes, but they are more specific in Portuguese.

• fritar = to fry
• cozinhar = to cook, often to boil or to cook through

So in this sentence:

• fritar o alho = fry the garlic
• cozinhar o arroz = cook the rice

English uses cook very broadly, but Portuguese often chooses a more specific verb depending on the method.

It is natural, yes, especially if you mean frying the garlic in oil.

But in recipes, you may also see other verbs depending on the exact action:

• fritar o alho = fry the garlic
• dourar o alho = brown the garlic
• refogar o alho = sauté the garlic

In real Brazilian cooking language, refogar is extremely common when garlic or onion is cooked briefly in oil before adding other ingredients.

So this sentence is fine, but depending on the recipe, a Brazilian might also say:

• Depois que eu refogar o alho, vou cozinhar o arroz.

Yes, it is the normal punctuation here.

The sentence begins with an adverbial clause:

• Depois que eu fritar o alho

and then comes the main clause:

• vou cozinhar o arroz

When that introductory clause comes first, Portuguese normally uses a comma:

• Depois que eu fritar o alho, vou cozinhar o arroz.

If the order were reversed, the comma is usually not needed:

• Vou cozinhar o arroz depois que eu fritar o alho.

Then you would not use the future subjunctive here.

For example:

• Depois que eu fritei o alho, cozinhei o arroz.
  After I fried the garlic, I cooked the rice.

Or in a more conversational style:

• Depois que eu fritei o alho, fui cozinhar o arroz.

The important contrast is:

• future situation: depois que eu fritar
• past situation: depois que eu fritei

So the form fritar in the original sentence is specifically tied to a future, not-yet-completed action.