Learn Hardcore Portuguese (Portugal): O atendimento foi rápido depois de chamarem a minha senha. - The service was fast after they called my number.

It means the “service/assistance” you received at a counter, desk, clinic, etc. It’s about being attended to, not “attendance” in the school sense. The verb is atender (“to attend to/serve”), and the noun o atendimento is the act or quality of that service.

Why do we need the article o in o atendimento?

Portuguese uses definite articles a lot more than English. Here o atendimento points to that specific instance of service you experienced. Saying just atendimento foi rápido is ungrammatical in Portuguese.

Why is it foi rápido and not era rápido or estava rápido?

Foi (preterite) presents a completed fact: the service was quick (on that occasion).

Era rápido (imperfect) would describe an ongoing or habitual background quality.
Estava rápido is rare/natural only in specific contexts and usually suggests a temporary state at that moment; here the preterite is the idiomatic choice.

Should it be rápido or rapidamente?

Here rápido is a predicate adjective agreeing with the subject (o atendimento) after the copula foi: “the service was quick.”
If you want the adverb, you’d change the structure: Atenderam-me rapidamente or O atendimento foi feito rapidamente.

Why is it rápido (masculine) and not rápida?

Agreement: atendimento is a masculine noun, so the predicate adjective matches it: rápido. If the subject were feminine, you’d use rápida.

What does senha mean in Portugal? Isn’t it “password”?

In Portugal, senha commonly means a queue ticket/number at a service counter. For “password,” European Portuguese prefers palavra‑passe (though many speakers also say senha in tech contexts). In this sentence, senha clearly means “ticket number.”

Why is it a minha senha and not just minha senha?

In European Portuguese, possessives almost always take the definite article: o meu / a minha. So a minha senha is the normal form. Dropping the article (minha senha) is typical of Brazilian usage, not European.

Is the a in a minha senha a preposition or an article?

It’s the feminine definite article a (“the”). The verb chamar takes a direct object with no preposition here: chamar a senha / chamar a minha senha (“to call the number/my number”).

Why depois de chamarem and not depois chamaram?

Because depois de is a preposition; it must be followed by a noun or an infinitive. So you use the infinitive: depois de chamarem…
If you want a finite clause, you’d restructure: Depois que chamaram… (Brazilian), or in EP: Depois de chamarem…, or simply start a new sentence: Chamaram a minha senha e o atendimento foi rápido.

What is chamarem? Why that form?

It’s the personal infinitive, 3rd person plural: “they (to) call.” Portuguese uses the personal infinitive to show who the (implicit) subject of the infinitive is. Here it means “after they called.” It’s very natural in EP, especially when the subject of the infinitive is different from the main clause’s subject.

Could I use depois de terem chamado instead?

Yes: depois de terem chamado a minha senha (perfect/past infinitive) is also correct. It makes the prior completion explicit. Both depois de chamarem and depois de terem chamado work here; the latter is a bit more explicit/formal.

Is depois de chamar a minha senha (without -em) OK?

Grammatically it can occur, but it’s ambiguous about who did the calling and often suggests the same subject as the main clause. Since the caller is “they/people at the counter,” EP prefers the personal infinitive to mark that: depois de chamarem a minha senha. That avoids ambiguity.

Can I say depois de me chamarem instead of depois de chamarem a minha senha?

Yes. Depois de me chamarem = “after they called me.” It’s idiomatic and a bit more personal. In EP with infinitives after prepositions, the clitic can appear before or after, but depois de me chamarem is the most common; depois de chamarem‑me is also accepted.

Is chamar por alguém used here?

Not in this context. Chamar alguém = “to call someone,” and for numbers you say chamar a senha. Chamar por alguém tends to mean “call out for someone” (cry out), not “call a queue number.”

Is there a passive alternative?

Yes, more formal: Depois de a minha senha ser chamada, o atendimento foi rápido. You could also front it: Depois de ser chamada a minha senha, o atendimento foi rápido. The active with an implicit “they” (depois de chamarem…) is more natural in speech.

Can I move the depois de‑clause to the front?

Absolutely: Depois de chamarem a minha senha, o atendimento foi rápido. Same meaning; fronting the time clause is very common in Portuguese.