Eu gosto de andar no parque quando o tempo está bom.

Because gostar normally takes the preposition de in Portuguese.

• gostar de + noun
  • Eu gosto de música. = I like music.
• gostar de + infinitive
  • Eu gosto de andar. = I like to walk.

So Eu gosto de andar... is the natural structure.
A direct object without de would be incorrect here.

After gostar de, Portuguese uses the infinitive to express the activity someone likes doing.

• Eu gosto de andar. = I like walking / I like to walk.
• Ela gosta de ler. = She likes reading / She likes to read.

This works much like English like to walk or like walking. Portuguese does not use a gerund here the way English often does.

Yes. In many cases, Portuguese allows you to omit the subject pronoun because the verb form already shows who the subject is.

• Eu gosto de andar no parque...
• Gosto de andar no parque...

Both are correct.
Including Eu can add emphasis, clarity, or contrast.

For example:

• Eu gosto de andar, mas ele prefere correr.
  = I like walking, but he prefers running.

No is a contraction of em + o.

• em = in / at
• o = the
• no = in the / at the

So:

• no parque = in the park / at the park

Other common contractions:

• na = em + a
• nos = em + os
• nas = em + as

Examples:

• na praia = at the beach
• nos Estados Unidos = in the United States

Yes, tempo can mean both time and weather in Portuguese. Context tells you which meaning is intended.

In this sentence:

• quando o tempo está bom

it clearly means when the weather is nice/good.

Examples:

• Não tenho tempo. = I don’t have time.
• O tempo está ruim hoje. = The weather is bad today.

This is very common in Portuguese, so learners get used to it quickly.

Portuguese often uses estar for temporary conditions and ser for more permanent or essential characteristics.

Here, the sentence is talking about the current weather condition, which is temporary:

• O tempo está bom. = The weather is nice.

That is why estar is used.

Compare:

• Ele está feliz. = He is happy.
  temporary state
• Ele é feliz. = He is a happy person.
  more permanent characteristic

So o tempo está bom sounds natural because weather changes.

Here, andar means to walk or to stroll around, depending on context.

So:

• Eu gosto de andar no parque can mean
  • I like to walk in the park.
  • I like walking in the park.

If you want to be more specific about walking for exercise or leisure, Brazilians also often use caminhar:

• Eu gosto de caminhar no parque.

Both are natural, but caminhar can sound a bit more specifically like walking as an activity, while andar is a broader verb that can also mean to move around, to go, or to function in other contexts.

Yes, absolutely. That version is also correct and natural.

• Eu gosto de andar no parque quando o tempo está bom.
• Quando o tempo está bom, eu gosto de andar no parque.

The meaning stays basically the same.
The difference is mainly what you emphasize first:

• starting with Eu gosto... focuses first on what you like
• starting with Quando o tempo está bom... focuses first on the condition

This kind of clause movement is very common in Portuguese.

Because bom agrees with tempo, and tempo is a masculine noun.

• o tempo → masculine singular
• therefore: bom

Compare:

• O tempo está bom. = The weather is nice.
• A temperatura está boa. = The temperature is good.

So the adjective changes to match the noun’s gender and number.

A simple learner-friendly pronunciation guide would be:

• Eu gosto de andar no parque quando o tempo está bom
• roughly: eh-ooh GOHS-too jee ahn-DAR noo PAR-kee KWAN-doo oo TEM-poo es-TAH bohng

A few useful pronunciation notes:

• de often sounds like jee in many Brazilian accents when it comes before i or e sounds, though this varies.
• andar has stress on the last syllable: an-DAR
• parque is stressed on PAR
• quando is stressed on QUAN
• está is stressed on the last syllable: es-TA
• bom ends with a nasal sound, not a strong final m

Pronunciation varies across Brazil, but this will help you sound understandable.

It depends on what you mean.

• no parque = in the park / at the park
• na praça = in the square / at the plaza

So na praça changes the location.

As for ao parque, that usually suggests movement to the park rather than being in the park:

• Vou ao parque. = I’m going to the park.
• Ando no parque. = I walk in the park.

So in your sentence, no parque is the right choice because the walking happens there.

Yes. Portuguese is fairly flexible with this kind of time clause.

Possible versions:

• Eu gosto de andar no parque quando o tempo está bom.
• Quando o tempo está bom, eu gosto de andar no parque.
• Eu gosto de andar no parque com tempo bom.

That last one, com tempo bom, is a bit more compact and means something like in good weather, but your original sentence is clearer and very natural for learners.

So the original sentence is an excellent standard model.