Learn Hardcore Portuguese (Brazil): A técnica disse que o botão foi trocado em cinco minutos. - The technician said the button was replaced in five minutes.

In this sentence, a técnica is the feminine form meaning the (female) technician.
Portuguese técnica can also mean technique, but the context (someone said something) strongly points to a person here.
If the technician were male (or unspecified but grammatically masculine), you’d use o técnico.

What do the accents in técnica mean? Do I have to write them?

Yes—accents are part of the spelling in Portuguese. Técnica has an acute accent (é) to mark stress and vowel quality. Without the accent (tecnica), it’s considered a spelling error and can confuse readers.

Why does Portuguese use disse que? Can you drop que?

Que is the normal connector meaning that after verbs of saying/thinking: disse que = said that.
In standard Portuguese, you generally don’t drop que the way English sometimes drops that.

What tense is disse?

Disse is the pretérito perfeito (simple past) of dizer (to say/tell). It refers to a completed action in the past: she said.

Why is the second verb in foi trocado also in the past? How does this structure work?

Foi trocado is a passive voice construction:

foi = past of ser (to be) used as an auxiliary
trocado = past participle of trocar (changed/replaced)
So o botão foi trocado literally means the button was changed/replaced.

How do you know it’s passive voice and not just “was” as in a state?

Because ser + past participle is the typical pattern for a passive event (an action done to something): was replaced.
If you wanted to emphasize the resulting state, Portuguese often uses estar: o botão estava trocado (less common, and sounds odd here), or more naturally something like o botão já tinha sido trocado depending on meaning.

Why is it trocado (masculine) and not trocada?

Past participles in the passive agree with the noun they describe.
Botão is masculine singular (o botão), so you use trocado.
If it were a peça (feminine), you’d say a peça foi trocada.

Could you say this in active voice? What would it look like?

Yes. Active voice would name who did the action, for example:

A técnica trocou o botão em cinco minutos. = The technician replaced the button in five minutes.
The passive (o botão foi trocado) is used when the focus is on the button, or when the doer is unknown/irrelevant.

What does trocar mean exactly here—“change” or “swap”?

Trocar can mean to change, to replace, or to swap, depending on context.
With something like a button/component, trocar o botão is commonly understood as replace the button.

Is em cinco minutos “in five minutes” (duration) or “within five minutes” (deadline)?

It can be interpreted both ways, but the most common reading here is it took five minutes (duration).
If you want to be more explicit:

duration: em cinco minutos is common in Brazilian Portuguese
within a limit: dentro de cinco minutos = within five minutes

Why is the word order disse que o botão foi trocado and not something else?

Portuguese typically keeps a clear clause structure:

main clause: A técnica disse
subordinate clause introduced by que: o botão foi trocado em cinco minutos
You can rearrange for emphasis, but this is the neutral, most natural order.

How would you add “by someone” (agent) to the passive sentence?

You’d use por (or sometimes pelo/pela = por + o/a):

A técnica disse que o botão foi trocado pela equipe. = …was replaced by the team.
If the agent is unknown: foi trocado por alguém = was replaced by someone.