Depois do aquecimento, fazemos alongamento das pernas e dos braços.

In Portuguese, the preposition de often combines with the definite article:

• de + o = do
• de + a = da
• de + os = dos
• de + as = das

The noun aquecimento is masculine singular (o aquecimento).
To say after the warm-up, you need depois de + o aquecimento, which contracts to depois do aquecimento.

Depois de aquecimento (without the article) sounds strange here and is not the normal way to talk about this specific activity in European Portuguese.

Yes, you can say:

• Depois do aquecimento, fazemos...
• Após o aquecimento, fazemos...

They both mean after the warm-up.

Differences:

• Depois de / depois do is more common and more neutral in everyday speech.
• Após sounds a bit more formal or written, but it is perfectly correct and often used in instructions, manuals, or formal texts.

Both are grammatically possible, but they sound different:

• fazemos alongamento = literally we do stretching

  • Very common in gym / sports contexts.
  • Uses the verb fazer with a noun: fazer alongamento, fazer exercício, fazer treino.

• alongamos = we stretch (verb alongar used directly)

  • Also correct, but less commonly used in everyday gym instructions.
  • More likely in contexts like alongamos os músculos antes do treino.

So the sentence uses the very natural collocation fazer alongamento that you frequently hear from trainers or in fitness classes.

Two points:

1. Body parts normally take the definite article in Portuguese

   • as pernas, os braços, a cabeça, o pescoço
   • So das pernas = de + as pernas
   • dos braços = de + os braços

2. Using the article here is the default, natural pattern

   • alongamento das pernas e dos braços sounds normal and complete.
   • alongamento de pernas e braços is possible but sounds more technical, generic, or like a label/header.

In everyday European Portuguese, when talking about your own body, alongamento das pernas e dos braços is the standard, natural choice.

In Portuguese, with body parts, the possessor is usually understood from the context, so you normally use the definite article, not the possessive:

• Lavo as mãos. = I wash my hands.
• Doe-me a cabeça. = My head hurts.
• Massajou-lhe as costas. = He massaged his/her back.

In your sentence, fazemos alongamento das pernas e dos braços is clearly about our legs and arms, because the subject is we.

You would only say das nossas pernas / dos nossos braços if you needed special emphasis or contrast, for example:

• Não das pernas deles, mas das nossas pernas e dos nossos braços.
  (Not their legs, but our legs and our arms.)

The subject pronoun nós is optional in Portuguese.

• The verb ending in fazemos already tells you the subject is we (first person plural).
• So Nós fazemos alongamento... and Fazemos alongamento... both mean We stretch....

You add nós only for emphasis or contrast:

• Nós fazemos alongamento, eles não fazem.
  (We stretch, they don’t.)

The Portuguese present tense can express:

1. A habit / routine

   • Depois do aquecimento, fazemos alongamento...
     → After the warm-up, we (always/usually) stretch our legs and arms.

2. Instructions / sequence in a procedure

   • Like in a class plan: First we do X, then we do Y.

It usually does not mean right now at this exact moment (that would more typically be estamos a fazer alongamento in European Portuguese). In this sentence, it sounds like a routine or a general description of what happens after the warm-up.

Yes. Both are correct:

• alongamento das pernas e dos braços
• alongamento dos braços e das pernas

The meaning is the same: stretching both legs and arms. The order here is flexible and does not change the sense of the sentence.

Approximate European Portuguese pronunciations (stressed syllable in CAPS):

• aquecimento → ɐ-keh-see-MEN-too (the e in -men- is nasal)
• alongamento → ɐ-lon-gɐ-MEN-too (again, nasal -men-)
• pernas → PAIR-nɐsh (final -s often sounds like sh in European Portuguese)
• braços → BRAH-soosh (final -s → sh, open a in BRÁ-)

These are approximations to help an English speaker; real European Portuguese reduces many unstressed vowels more than English does.

Alongamento has a general meaning of lengthening / extension:

• In sport/fitness, it usually means stretching exercises:
  
  • fazer alongamento, exercícios de alongamento.
• In other contexts, it can mean:
  
  • Physical lengthening of something (e.g. alongamento de uma peça de roupa – making a piece of clothing longer).
  • Figurative extension (e.g. alongamento do prazo – extension of a deadline).

In your sentence, it is clearly the fitness meaning: stretching.