Não tenho sequer um minuto.

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

• tenho = I have
• so Não tenho... already clearly means I don’t have...

You can say Eu não tenho sequer um minuto, but eu is usually only added for emphasis, contrast, or clarity.

• Não tenho sequer um minuto. = neutral
• Eu não tenho sequer um minuto. = more emphatic, like I don’t even have a minute

Tenho is the present tense, first person singular, of the verb ter (to have).

Here is the relevant part of the conjugation:

• eu tenho = I have
• você tem = you have
• ele/ela tem = he/she has

So Não tenho... literally means I do not have...

That is the normal way to make a sentence negative in Portuguese.

• Tenho um minuto. = I have a minute.
• Não tenho um minuto. = I don’t have a minute.

So unlike English, Portuguese does not need do/does for negation. You just put não before the conjugated verb.

Sequer means even or not even, depending on the sentence.

In a negative sentence like this one, it adds emphasis:

• Não tenho sequer um minuto. = I don’t have even a minute. / I don’t have so much as a minute.

It makes the statement stronger than just Não tenho um minuto.

Yes, but it sounds a bit more formal or polished than some everyday alternatives.

In casual Brazilian Portuguese, people very often say:

• Não tenho nem um minuto.
• Não tenho nem sequer um minuto.

These are very natural in speech.
Sequer by itself is perfectly correct and natural, but it can sound slightly more literary or emphatic than nem.

They are related, but not identical.

• sequer = even / so much as
• nem = often not even / nor / neither
• nem sequer = stronger, very explicitly not even

Examples:

• Não tenho sequer um minuto. = I don’t even have a minute.
• Não tenho nem um minuto. = same basic idea, very common in speech.
• Não tenho nem sequer um minuto. = even more emphatic: I don’t have not even a single minute.

In everyday Brazilian speech, nem um minuto is extremely common.

Because the sentence is talking about not even one minute.

• um minuto = one minute / a minute

The singular is used because the idea is not even a single minute.
If you said minutos, the meaning would be less precise in this structure.

Compare:

• Não tenho um minuto. = I don’t have a minute.
• Não tenho sequer um minuto. = I don’t have even a minute.
• Não tenho minutos sobrando. = I don’t have minutes to spare.

Yes. Não tenho nenhum minuto is grammatical, though it is not the most idiomatic version for this exact idea.

Compare the nuance:

• Não tenho sequer um minuto. = I don’t have even a minute.
• Não tenho nem um minuto. = very natural, common spoken alternative
• Não tenho nenhum minuto. = literally I don’t have any minute, which is understandable but less idiomatic than the first two

In Brazilian Portuguese, for this kind of emphasis, nem um minuto or sequer um minuto sounds more natural.

It usually goes before the word or phrase it emphasizes.

Here, it emphasizes um minuto:

• Não tenho sequer um minuto.

This is the most natural placement.

You may also hear:

• Não tenho nem sequer um minuto.

That is also very natural.

Placing sequer elsewhere may sound awkward or change the rhythm of the sentence, so it is best to learn sequer um minuto as a chunk.

In Brazilian Portuguese, sequer is roughly pronounced like:

• seh-KEHR

A few notes:

• the stress is on the second syllable: se-QUER
• the final r in Brazil often sounds like a soft guttural h sound, depending on the region
• so in many accents it may sound close to seh-KEH(r/h)

It is one word: sequer, not se quer.

No. They are different.

• sequer = an adverb meaning even / not even
• se quer = two words, usually meaning something like if you want or part of another structure involving querer

Examples:

• Não tenho sequer um minuto. = I don’t even have a minute.
• Se quer sair, avise. = If you want to leave, let me know.

So in your sentence, it must be the one-word form: sequer.

Yes. It is correct and natural.

It sounds like something a Brazilian speaker might say when emphasizing how busy they are. Depending on the situation, a more colloquial spoken version might be:

• Não tenho nem um minuto.
• Tô sem nem um minuto. (more informal)
• Não tenho nem tempo. (very common and natural)

But Não tenho sequer um minuto is absolutely good Portuguese and sounds strong and clear.