Eu vou pedir para o técnico consertar o botão amanhã.

In Brazilian Portuguese, ir (vou) + infinitive is the most common way to talk about a near or planned future, similar to I’m going to… in English: Eu vou pedir….
Pedirei is grammatically correct, but it’s more formal and less common in everyday speech.

Pedir para + [person] + [infinitive] means to ask [person] to do [verb].
So pedir para o técnico consertar = ask the technician to fix.

A very common alternative structure is:

• Eu vou pedir que o técnico conserte o botão amanhã.
  Here pedir que is followed by subjunctive (conserte).

Both exist, and both are common:

• Eu vou pedir para o técnico consertar… (very common in Brazil)
• Eu vou pedir ao técnico para consertar… (also correct; slightly more “complete” because it marks the person with a + o = ao)

In practice, many Brazilians naturally use pedir para + person + infinitive.

Because técnico is masculine here. The article must match the gender:

• o técnico (male technician)
• a técnica (female technician)

So you could also say:

• Eu vou pedir para a técnica consertar o botão amanhã.

Yes. In Brazilian Portuguese, para o is very often reduced to pro in informal speech and writing:

• Eu vou pedir pro técnico consertar o botão amanhã.

Similarly:

• para a → pra
• para os → pros
• para as → pras

Because this sentence uses the infinitive after pedir para:

• pedir para [alguém] consertar (infinitive)

If you use pedir que, then you typically use the subjunctive:

• Vou pedir que o técnico conserte o botão.

Both are correct; they’re just different structures.

Both can translate as to fix, but:

• consertar = to repair (more clearly about fixing something broken)
• arrumar = to fix/tidy/arrange (broader; can mean repair in casual speech)

For a broken button, consertar is the most precise.

Portuguese uses articles a lot, and o often points to a specific known item:

• o botão = the button (the one we’re talking about: on a device, shirt, elevator, etc.)

If it were not specific, you might use:

• um botão = a button (some button, not previously identified)

It can be interpreted either way, but most often it’s understood as the time for the overall plan (commonly the fixing, or at least the action starting tomorrow). If you want to remove ambiguity, you can specify:

• Asking tomorrow: Amanhã eu vou pedir para o técnico consertar o botão.
• Fixing tomorrow: Eu vou pedir para o técnico consertar o botão amanhã mesmo. / …consertar amanhã.

Context usually makes it clear.

Yes. These are all natural, with slightly different emphasis:

• Eu vou pedir para o técnico consertar o botão amanhã. (neutral)
• Amanhã eu vou pedir para o técnico consertar o botão. (emphasizes tomorrow)
• Eu vou amanhã pedir para o técnico consertar o botão. (possible, but less natural in everyday speech)

técnico is a good general word for a repair/service technician (appliance, internet, electronics, etc.). Depending on context, you might also hear:

• conserto / assistência técnica (repair service / service center)
• mecânico (mechanic, usually for vehicles)
• manutenção (maintenance; often in phrases like técnico de manutenção)

But o técnico is a very common, natural choice.

You need a linking structure. Pedir o técnico consertar is not standard Portuguese. Use one of these:

• pedir para o técnico consertar…
• pedir ao técnico para consertar…
• pedir que o técnico conserte…

Those are the natural grammatical options.

A more formal version might use the simple future and/or pedir que:

• Pedirei que o técnico conserte o botão amanhã.
  Or:
• Vou solicitar que o técnico conserte o botão amanhã. (more formal vocabulary: solicitar)