Depois que cortar a abóbora, eu vou guardar a outra metade na geladeira.

Here cortar is best understood as the future subjunctive, not the infinitive.

After expressions like depois que, quando, and se, Portuguese often uses the future subjunctive when talking about a future action:

• Depois que eu cortar... = after I cut...
• Quando ele chegar... = when he arrives...
• Se eles vierem... = if they come...

The confusing part is that for regular -ar verbs, the future subjunctive looks exactly like the infinitive:

• infinitive: cortar
• future subjunctive: quando eu cortar

So even though the form is the same, the grammar function is different here.

Yes, Depois que eu cortar a abóbora is a fuller, very clear version.

In Portuguese, the subject is often omitted when it is understood from context. In this sentence, the main clause has eu vou guardar, so it is easy to understand that the person who will cut the pumpkin is also eu.

So both are possible:

• Depois que eu cortar a abóbora, eu vou guardar...
• Depois que cortar a abóbora, eu vou guardar...

The version with eu before cortar is more explicit. The version without it is more compact and can sound natural in speech.

Yes. Depois de cortar a abóbora is also correct and natural.

There is a small structural difference:

• Depois de + infinitive
  Depois de cortar a abóbora, vou guardar...

• Depois que + future subjunctive
  Depois que eu cortar a abóbora, vou guardar...

Both can mean after cutting / after I cut the pumpkin.

A useful rule of thumb:

• use depois de + infinitive for a more compact structure
• use depois que + verb when you want a full clause

In everyday Brazilian Portuguese, both are common.

Because ir + infinitive is extremely common in spoken Brazilian Portuguese for future meaning.

So:

• eu vou guardar = I’m going to store / I will store
• guardarei = I will store

Both are correct, but they feel different:

• eu vou guardar sounds more natural in everyday conversation
• guardarei sounds more formal, more written, or more literary

A native speaker would very often choose vou guardar in normal speech.

Yes, and in this context that fits well.

Guardar often means:

• to keep
• to store
• to put away

With food, guardar na geladeira usually means to put it in the fridge to keep it there.

That is slightly different from colocar na geladeira, which focuses more on the physical act of putting it there.

So:

• colocar na geladeira = put it in the fridge
• guardar na geladeira = store it in the fridge / put it away in the fridge

In this sentence, guardar suggests saving the other half for later.

Portuguese uses definite articles more often than English.

In this sentence:

• a abóbora = the pumpkin being dealt with
• a outra metade = the other half of that same pumpkin
• na geladeira = in the refrigerator

English sometimes omits an article where Portuguese keeps one, but in Portuguese these articles sound very natural and expected.

Also, na is not a separate article by itself. It is a contraction:

• em + a = na

So:

• na geladeira literally comes from em a geladeira

Because a outra metade is the natural way to say the other half.

When something is divided into two equal parts, Portuguese usually refers to one part and the other half:

• Comi metade e guardei a outra metade.

Segunda metade usually means second half in a sequence, especially with time or organized parts:

• a segunda metade do jogo = the second half of the game
• a segunda metade do filme = the second half of the movie

So for a pumpkin cut into two pieces, a outra metade is the better choice.

Na geladeira means in the refrigerator / in the fridge.

The word na is a contraction:

• em = in
• a = the
• em + a = na

Because geladeira is feminine, the contraction is na.

Compare:

• no armário = in the cabinet (em + o)
• na geladeira = in the fridge (em + a)

So this is a very common Portuguese pattern.

Yes. You could say:

Depois que cortar a abóbora, vou guardar a outra metade na geladeira.

Portuguese often drops subject pronouns when the meaning is clear. So vou guardar already tells us the subject is I.

Keeping eu can still be useful:

• for emphasis
• for contrast
• for clarity

For example:

• Eu vou guardar a outra metade, mas você pode usar o resto.

In your sentence, eu is optional, but perfectly natural.

Because abóbora is a feminine noun in Portuguese, so it takes feminine forms:

• a abóbora
• a outra metade

Portuguese noun gender is something you usually have to learn with each word. Sometimes the ending helps, but not always. In this case, abóbora is simply a feminine noun, so the article is a.

That is why the sentence says:

• a abóbora not
• o abóbora