A sala em que estudamos fica perto da biblioteca.

Because the idea needs the preposition em: you study in a room. In Portuguese, when a relative clause needs a preposition, the preposition stays there:

a sala em que estudamos

So this is like the room in which we study. Using only que here would not be standard.

Yes. A sala onde estudamos is very natural, because onde is commonly used for places.

• em que = correct, slightly more neutral or formal
• onde = very common and natural for places

Both work well here.

Yes. A sala na qual estudamos is grammatically correct.

However, na qual sounds more formal and is more common in careful writing than in everyday speech. In normal conversation, people are more likely to say onde or em que.

Because Portuguese often leaves out subject pronouns. The verb ending already shows the subject.

Estudamos already tells you the subject is we.

You can say nós estudamos if you want emphasis or contrast, but it is not necessary here.

Yes. With -ar verbs, the we form in the present and the simple past can be identical:

• estudamos = we study
• estudamos = we studied

Context tells you which one is meant. In this sentence, the present meaning is the natural one because fica is also in the present.

Not usually, if you want to emphasize that it is happening right now. In European Portuguese, the usual way is:

estamos a estudar

So:

• estudamos = we study / we do study
• estamos a estudar = we are studying

In this sentence, estudamos sounds right because it describes the room as the place where we study in general.

Ficar is very commonly used to talk about location, especially where something is situated.

So A sala fica perto da biblioteca means something like The room is located near the library.

Está can also mean is, but fica is especially natural for a stable location like a room, building, shop, or town.

Perto normally combines with de:

perto de = near

Then de + a contracts to da:

• de + a biblioteca → da biblioteca

So:

perto da biblioteca = near the library

Because Portuguese uses definite articles more often than English.

Here, a biblioteca = the library. After de, it becomes da biblioteca.

In English, you sometimes omit the where Portuguese would naturally keep the article.

It describes a sala.

So the structure is:

• A sala = the room
• em que estudamos = in which we study

Together: the room in which we study

The relative clause comes right after the noun it describes.

No. That changes what the relative clause refers to.

• A sala em que estudamos fica perto da biblioteca
  = the place where we study is the room

• A sala fica perto da biblioteca onde estudamos
  = the place where we study is the library

So the position of the clause changes the meaning.