Nós deixamos o carro no parque e vamos a pé para casa.

In European Portuguese, deixamos (without an accent) is present tense:

• (presente do indicativo): nós deixamos = we leave / we are leaving

The past (pretérito perfeito) is written with an accent: deixámos:

• nós deixámos = we left

So:

• Nós deixamos o carro no parque… → We leave the car in the car park… (habitually, or right now)
• Nós deixámos o carro no parque… → We left the car in the car park… (completed past action)

In speech, the difference is subtle, but in writing the accent clearly marks the past tense.

You can absolutely drop Nós:

• Deixamos o carro no parque e vamos a pé para casa.

Portuguese is a “null subject” language: the verb ending -mos already tells you it’s we.

You typically keep Nós when you want to:

• Emphasise the subject:
  Nós deixamos o carro…, mas eles vão de autocarro.
  We leave the car…, but they go by bus.
• Avoid ambiguity in more complex sentences.

In a neutral context, both are correct; without Nós sounds a bit more natural in everyday speech.

You can’t drop the article here in standard Portuguese. Carro almost always needs an article or a determiner:

• o carro – the car (a specific one we know about)
• um carro – a car (some car, not specified)
• meu carro / o meu carro – my car / my car (with article, which is very common in European Portuguese)

Bare carro without any article would sound wrong in this sentence.

So:

• ✅ Deixamos o carro no parque.
• ⛔ Deixamos carro no parque. (unnatural / incorrect)

Literally, no parque is:

• em + o parque → no parque = in the park / at the park

However, in European Portuguese, parque is very often short for:

• parque de estacionamento = car park / parking lot

So in Portugal:

• Deixamos o carro no parque.
  is usually understood as
  We leave the car in the car park.

If you wanted trees/grass park, context or wording would usually make it clear, e.g.:

• Deixamos o carro no parque da cidade. – We leave the car in the city park.

A pé is a fixed expression meaning “on foot”:

• ir a pé – to go on foot
• voltar a pé – to return on foot

The a here is a preposition that historically expresses manner (by, on), similar to English on in “on foot”.

You cannot usually replace it with other prepositions:

• ⛔ ir em pé – this means “to go standing up” (e.g. standing on a bus), not “on foot”.
• ⛔ ir de pé – not idiomatic.

So you should learn a pé as a chunk:
vamos a pé = we go on foot / we walk.

Both are grammatically correct:

• vamos a pé para casa
• vamos para casa a pé

Portuguese word order is relatively flexible, especially with adverbial phrases like a pé and para casa.

Subtle differences:

• vamos a pé para casa – slightly emphasises the manner first (we go *on foot home*).
• vamos para casa a pé – slightly emphasises the destination first (we go *home, on foot*).

In everyday speech, both versions sound natural, and the difference is minimal.

In Portuguese there’s a distinction between casa = home and a casa = the house.

• para casa → (to) home (no article)
• para a casa → to the house (specific building)

So:

• Vamos a pé para casa. – We walk home.
  (general idea of home, like English go home without “to”.)
• Vamos a pé para a casa da Maria. – We walk to Maria’s house.
  (a specific house, so it takes the article)

Similarly:

• Estou em casa. – I’m at home.
• Estou na casa da minha mãe. – I’m at my mother’s house.

You can, but there’s a nuance:

• Caminhamos para casa.
  = We walk home. (more literally using the verb caminhar)

• Vamos a pé para casa.
  = We go home on foot / we walk home. (using ir

  • a pé)

Differences:

• caminhar often has a flavour of to walk (as an activity), to stroll, or to walk for exercise, especially in European Portuguese.
• ir a pé is the most common, neutral way to say you’re going somewhere by walking, as opposed to de carro, de autocarro, de comboio, etc.

So Vamos a pé para casa is the most natural, everyday way to say We walk home.

Yes. Portuguese often uses the present tense for future plans, especially when the context makes it clear it’s about the future:

• Amanhã nós deixamos o carro no parque e vamos a pé para casa.
  = Tomorrow we’ll leave the car in the car park and walk home.

Without a time expression (like amanhã, depois, etc.), it’s more naturally understood as:

• a habitual action: We (usually) leave the car… and (then) walk home.
• or a description of what we’re doing now.

For a clearly future meaning, you can also say:

• Amanhã vamos deixar o carro no parque e vamos a pé para casa.
  (using vamos deixar = we’re going to leave)

Yes, you can:

• Deixamos o carro no estacionamento.

In Portugal:

• parque (de estacionamento) and estacionamento can both mean car park / parking lot.
• parque by itself is very commonly used for a car park, especially if context makes it obvious.

In Brazil, however:

• estacionamento is the usual word for car park.
• parque normally means a park (with trees, playgrounds, etc.), not a parking lot.

So in European Portuguese both are fine, but your original sentence with no parque is very idiomatic.