Pedi licença médica antes de tirar férias.

Pedi is the 1st person singular form of pedir in the pretérito perfeito (simple past / preterite).

• pedir = to ask for, request
• eu pedi = I asked for / I requested

In this sentence, it describes a completed action in the past.

In Brazilian Portuguese, the subject pronoun is often omitted when the verb form already makes the subject clear.

• Pedi already tells you the subject is eu (I).
• So Pedi licença médica... naturally means I requested sick leave...

You can include eu for emphasis, contrast, or clarity:

• Eu pedi licença médica, não o Carlos.
  = I requested sick leave, not Carlos.

Licença médica means medical leave or sick leave.

• licença = leave, permission, absence officially allowed
• médica = medical

So the phrase refers to time away from work or duties for health reasons, usually with medical justification.

Because médica agrees with licença, which is a feminine noun.

In Portuguese, adjectives usually agree with the noun in gender and number:

• licença = feminine singular
• therefore: médica = feminine singular

So:

• licença médica = correct
• licença médico = incorrect

After antes de, Portuguese normally uses an infinitive when the subject of both actions is the same.

So:

• antes de tirar férias = before taking vacation

Here, the same person both:

1. requested medical leave
2. took vacation

That is why the infinitive tirar is used.

Compare:

• Pedi licença médica antes de tirar férias.
  = I requested sick leave before taking vacation.

But if the subject changes, Portuguese often uses a clause:

• Pedi licença médica antes de ele tirar férias.
  = I requested sick leave before he took vacation.

In Brazilian Portuguese, tirar férias is a very common expression meaning to take vacation / to go on vacation.

Literally, tirar often means to take, remove, or pull out, but in many expressions it has an idiomatic meaning.

So you should learn tirar férias as a set phrase.

Other possible expressions exist, but tirar férias is one of the most natural and common in Brazil.

In Portuguese, férias is normally used as a plural noun, even when English would often use singular vacation.

So:

• tirar férias = to take vacation / to go on vacation
• as férias = the vacation / the vacation period

This is just how the noun works in Portuguese, much like some English nouns that are usually plural in form.

After tirar, it is very common to say simply tirar férias without an article.

• tirar férias = to take vacation

You may also hear tirar as férias in some contexts, especially when referring to a specific vacation period, but tirar férias is very natural and common as a general expression.

So in this sentence, no article is perfectly normal.

Yes. Licença médica usually sounds more official or administrative than simply saying someone was sick.

It often suggests:

• leave from work
• medical justification
• a formal or recognized absence

So it is closer to medical leave or sick leave than just illness by itself.

Usually, yes: the sentence presents the medical leave as happening before the vacation.

So the normal reading is:

1. the person requested medical leave
2. later, the person took vacation

However, the sentence itself mainly states the sequence of events. It does not explain why the person did this, or give more details about whether the leave and vacation were related.