Learn Hardcore Portuguese (Portugal): Sem esse carimbo oficial, a autorização de entrada no país não é válida. - Without that official stamp, the authorization to enter the country is not valid.

Sem esse carimbo oficial = Without that official stamp.
It’s used in many everyday expressions:
- sem açúcar = without sugar
- sem problema = no problem / without a problem

Most of the time, you can safely translate sem as without, though in some idiomatic expressions it may be rendered differently in English (e.g., sem dúvida = without a doubt / certainly).

Why is it esse carimbo and not este carimbo or aquele carimbo?

Portuguese has three main demonstratives:

este / esta – this, usually closer to the speaker
esse / essa – that, often closer to the listener or already known in context
aquele / aquela – that over there, more distant (physical or metaphorical)

In esse carimbo oficial, the idea is often that both speaker and listener already know which stamp is being referred to (for example, a specific immigration stamp), so esse is natural.

In European Portuguese, esse is very commonly used even when English might just say this or that, so the division is not always one‑to‑one with English.

What exactly does carimbo mean here? Is it the act of stamping or the stamp mark?

Carimbo can refer to:

The physical stamp tool (like a rubber stamp).
The stamp mark or impression it leaves on a document.

In esse carimbo oficial, it usually means the official stamp mark on your document (e.g., the immigration stamp in your passport) rather than the stamping device itself. Context tells you which sense is intended.

Can I change the word order and say: A autorização de entrada no país não é válida sem esse carimbo oficial?

Yes, that is perfectly correct and very natural.

Original: Sem esse carimbo oficial, a autorização de entrada no país não é válida.
Alternative: A autorização de entrada no país não é válida sem esse carimbo oficial.

Both mean the same thing.
Placing Sem esse carimbo oficial at the beginning just emphasizes the condition (the absence of the stamp).

Why is it autorização de entrada and not autorização para entrar?

Both are possible, but they have slightly different structures:

autorização de entrada = literally authorization of entry, using the noun entrada.
autorização para entrar = authorization to enter, using the verb entrar.

In formal or bureaucratic language (like immigration and legal texts), Portuguese often prefers noun + de + noun structures:

autorização de residência = residence permit
autorização de trabalho = work permit
autorização de entrada = entry authorization

So autorização de entrada no país sounds more formal and official, which fits this context.

What does no país literally mean, and why is it not em o país?

No is a contraction of em + o (in / on + the):

em + o = no
em + a = na

So no país literally means in the country.
Writing em o país is grammatically correct in theory, but in normal Portuguese you must contract it to no. The uncontracted form sounds wrong in everyday language.

Why is it não é válida and not não está válida? What is the difference between ser and estar here?

Ser and estar both translate as to be, but they have different uses:

ser (é válida) is used for more inherent, official, or defining characteristics.
estar (está válida) is used for more temporary states or conditions.

For documents, permissions, and validity, Portuguese almost always uses ser:

O bilhete é válido até amanhã. = The ticket is valid until tomorrow.
A autorização não é válida sem esse carimbo. = The authorization is (officially) not valid.

Using estar válida could suggest a more temporary, changeable state and sounds odd in a legal/administrative sense. The idea of valid / invalid as an official status tends to go with ser.

Why is válida feminine? How does agreement work here?

Válida is an adjective, and in Portuguese, adjectives must agree in gender and number with the noun they describe.

autorização is a feminine singular noun (a autorização).
So the adjective must also be feminine singular: válida.

Other examples:

O bilhete é válido. (masculine singular)
A autorização é válida. (feminine singular)
Os bilhetes são válidos. (masculine plural)
As autorizações são válidas. (feminine plural)

Why do we say de entrada no país instead of para entrar no país after autorização?

Both can be used, but they differ slightly in style:

autorização de entrada no país – more formal/legal, using the noun entrada.
autorização para entrar no país – a bit more neutral/everyday, using the verb entrar.

In immigration or official documentation, de entrada no país sounds more bureaucratic and technical, which is why it fits this sentence.

Is país here any country, or does it usually mean “this country” (the one we are in)?

On its own, o país just means the country in a general sense.
However, in a context like immigration or border control, o país usually refers to the specific country whose border you are entering – that is, the country we’re talking about now / the country you’re trying to enter.

So in practice, entrada no país is understood as entry into this country (the relevant one in the situation).