Después de que la bibliotecaria revise mi carné, sacaré dos libros más para el fin de semana.

Because después de que usually triggers the subjunctive when the action has not happened yet or is still viewed as future.

Here, the librarian has not checked the card yet, so Spanish uses:

• Después de que la bibliotecaria revise mi carné...

If the checking were already completed in the past, you would normally use the indicative:

• Después de que la bibliotecaria revisó mi carné, saqué dos libros más.

So revise is not present tense here; it is present subjunctive.

Not here. This is a common false friend.

In this sentence, revisar means to check, inspect, or look over.

So la bibliotecaria revise mi carné means the librarian checks my card, not that she revises/edits it.

Because it is the action the speaker says they will do later, after the librarian checks the card.

• sacaré = I will take out / I will check out

Spanish often uses the simple future for this kind of sequence. It sounds natural and clear.

You could also hear other future expressions in everyday speech, such as:

• voy a sacar dos libros más
• sometimes even the present: saco dos libros más, if the future meaning is obvious from context

But sacaré is perfectly good and natural.

Here sacar means to check out, take out, or borrow books from the library.

In Spain, sacar libros is a very natural way to talk about getting books from a library. It does not just mean physically removing them from somewhere.

So in this context:

• sacar libros = to check out / borrow books

Carné means a card, usually an ID or membership card.

In this sentence, mi carné is understood as my library card.

In Spain, carné is very common for things like:

• carné de estudiante = student card
• carné de socio = membership card
• carné de la biblioteca = library card

So here the full idea is simply that the librarian checks the speaker’s card before allowing the loan.

Because Spanish often omits subject pronouns when the verb ending already shows who the subject is.

• sacaré already tells you it means I will take out

So yo is unnecessary unless you want emphasis or contrast.

For example:

• Sacaré dos libros más. = neutral
• Yo sacaré dos libros más. = more emphatic, maybe contrasting with someone else

Because in Spanish, when más means more after a number, it normally comes after the noun phrase:

• dos libros más = two more books

Compare:

• más libros = more books
• dos libros más = two more books

So the position of más changes the structure:

• más + noun = more noun(s) in general
• number + noun + más = that many more noun(s)

Because para expresses the intended use or purpose.

Here, the idea is that the speaker is taking out the books for the weekend, meaning to have them available or read them over that time.

So para el fin de semana means something like:

• intended for the weekend
• to use/read during the weekend

Using por here would sound unnatural for this meaning.

Not with the same meaning.

Después de + infinitive is normally used when the subject is the same as in the main clause.

So:

• Después de revisar mi carné, sacaré dos libros más

sounds like I am the one checking my own card.

But in the original sentence, the one who checks the card is the librarian, not the speaker. Because the subjects are different, Spanish uses:

• Después de que + conjugated verb
• Después de que la bibliotecaria revise mi carné...

Because Spanish normally uses an article with a noun like this when it is the subject of the verb.

• la bibliotecaria = the librarian

Without the article, bibliotecaria would not work naturally here as a normal subject noun.

You could change the meaning slightly with another determiner, for example:

• una bibliotecaria = a librarian
• mi bibliotecaria = my librarian

But in the original sentence, la bibliotecaria is the normal form.