Learn Hardcore Portuguese (Portugal): O chefe vai avaliar a qualidade dos relatórios, nos quais a quantidade de erros deve ser mínima. - The boss will assess the quality of the reports, in which the number of errors must be minimal.

It refers back to relatórios (reports), which is masculine plural. Nos = em + os (“in the”), and quais is the relative pronoun that must agree in gender and number with its antecedent.

Masculine singular: no qual
Feminine singular: na qual
Masculine plural: nos quais
Feminine plural: nas quais

Can I replace nos quais with em que or onde?

em que is perfectly fine and more neutral: ..., em que a quantidade de erros deve ser mínima.
nos quais is a bit more formal/explicit.
onde is best reserved for places. Many speakers use it loosely, but for non-places like reports, careful/edited Portuguese prefers em que or nos quais.

Why is there a comma before nos quais? Does removing it change the meaning?

Yes. With the comma, the relative clause is non-restrictive (extra information): the requirement applies to the reports as a whole. Without the comma, it’s restrictive: it would mean “the reports in which the number of errors must be minimal,” i.e., only that subset of reports. So:

With comma: adding a comment about the reports.
Without comma: specifying which reports.

Why dos relatórios and why the definite articles (like a qualidade, a quantidade)?

dos is the contraction of de + os (“of the”).
Portuguese uses definite articles more freely than English, including with abstract nouns and when referring to a specific, known set.
a qualidade dos relatórios = “the quality of the reports” (specific set).
de relatórios (“of reports” in general) would sound odd here.
Dropping the article in a qualidade is typically only seen in titles/headings (telegraphic style), not in full sentences.

Why is mínima feminine singular? Shouldn’t it agree with erros?

The adjective agrees with the subject of the clause, which is a quantidade (feminine singular), not with erros (which is inside the prepositional phrase de erros). Hence mínima.

Compare: A percentagem de falhas é baixa. (adjective agrees with percentagem, not falhas)
Be careful: erros mínimos means “errors of minimal gravity/size,” not “a very small number of errors.”

Could I say deve ser o mínimo possível instead of deve ser mínima?

Yes. Both are correct:

… a quantidade de erros deve ser mínima.
… a quantidade de erros deve ser o mínimo possível. The second slightly intensifies the idea (“as low as possible”). You can also say o mais baixo possível.

Is quantidade de erros the same as número de erros?

Both are acceptable. número highlights a count and can feel a touch more precise; quantidade is broader and very common.

A quantidade de erros deve ser mínima.
O número de erros deve ser mínimo. Note the agreement: mínimo agrees with número (masc. sg.), while mínima agrees with quantidade (fem. sg.).

What’s the difference between vai avaliar, avaliará, and irá avaliar?

vai avaliar (ir + infinitive): the most common future in speech; neutral, often “planned/near” future.
avaliará (simple future): more formal/literate; common in writing, headlines, official texts.
irá avaliar (irá + infinitive): also formal, adds a slight sense of certainty or scheduled plan.

Does deve ser mean “must”? How does it compare to tem de/que ser or é para ser?

deve ser = “should/ought to be” (expectation or guideline; softer than “must”).
tem de ser = strong obligation (“has to be”); tem que ser is very common in speech, though de is the traditional/standard form.
é para ser = “is meant/supposed to be” (instructional/plan-based requirement).

Can I use just que here (without the preposition)?

No. The meaning requires “in which,” so you need the preposition em with a relative: em que, or the compound form nos quais. Plain que would be ungrammatical or change the meaning.

Can I rewrite the sentence without a relative clause?

Yes, for example:

O chefe vai avaliar a qualidade dos relatórios. Neles, a quantidade de erros deve ser mínima.
O chefe vai avaliar os relatórios; neles, a quantidade de erros deve ser mínima. These keep the meaning while avoiding the relative clause.

Should it be estar mínima instead of ser mínima?

Use ser. Here you’re classifying/setting a standard for the quantity (what it should be), so ser is natural. estar mínima is not idiomatic; if you meant a current state you might say está no mínimo, but that changes the meaning from a requirement to a description.

Is avaliar a qualidade dos relatórios different from avaliar os relatórios?

Slightly. avaliar a qualidade dos relatórios focuses the evaluation on quality specifically. avaliar os relatórios is broader (content, structure, findings, etc.). Both are fine, but the original makes the criterion explicit.

Any pronunciation tips (European Portuguese)?

chefe: initial ch is like English “sh.”
relatórios: rr is a throaty sound; stress on -tó-; final s sounds like “sh” in Portugal when not linking to a following vowel.
quais: sounds roughly like “kwai-sh.”
dos / nos: final s often sounds like “sh” in Portugal (becomes “z” when linking to a following vowel).
deve: open “e” in the first syllable, short final vowel.