O pacote que eu pedi pela internet chegou hoje de manhã.

Here que is a relative pronoun. It links o pacote to the clause eu pedi.

So the structure is:

• o pacote = the package
• que eu pedi = that I ordered / that I asked for

In English, que often translates as that, which, or sometimes it is left untranslated.

So:

• O pacote que eu pedi = The package that I ordered

Portuguese uses que very often in this kind of sentence.

Yes, it could be omitted.

Portuguese often drops subject pronouns when the verb ending already makes the subject clear. Since pedi clearly means I ordered / I asked for, you can say:

• O pacote que pedi pela internet chegou hoje de manhã.

That is completely natural.

Including eu is also fine. It can make the sentence a little clearer, a little more explicit, or slightly more conversational. Brazilian Portuguese uses subject pronouns more often than European Portuguese, so que eu pedi sounds very normal.

Pedi is the preterite form of pedir for eu:

• pedir = to ask for / to order
• eu pedi = I asked for / I ordered

In this sentence, it refers to a completed action in the past: you ordered the package, and that action is finished.

A quick conjugation of the preterite for pedir:

• eu pedi
• você/ele/ela pediu
• nós pedimos
• vocês/eles/elas pediram

So que eu pedi means that I ordered.

Yes — both ideas are connected.

Pedir literally means to ask for, but in many contexts that is exactly how Portuguese expresses to order something.

Examples:

• Pedi uma pizza. = I ordered a pizza.
• Pedi ajuda. = I asked for help.
• Pedi um livro pela internet. = I ordered a book online.

So in this sentence, pedi is naturally understood as ordered.

Because pedir takes a direct object when you ask for a thing.

You ask for something:

• pedir um pacote
• pedir um livro
• pedir ajuda

So the noun being referred to, o pacote, is the direct object of pedi. That is why Portuguese simply uses que:

• o pacote que eu pedi

If the verb required a preposition, then the relative pronoun would usually include it. But here it does not.

Pela internet means through the internet, over the internet, or more naturally in English, online.

So:

• pedi pela internet = I ordered online

It expresses the means or channel used to do the action.

In everyday Brazilian Portuguese, you may also hear:

• na internet
• online

These are all common, though they are not always exactly identical in nuance. In this sentence, pela internet sounds very natural.

Because pela is the contraction of:

• por + a = pela

And internet is commonly treated as a feminine noun in Portuguese:

• a internet

So:

• pela internet = through the internet

This kind of contraction is very common:

• por + o = pelo
• por + a = pela
• por + os = pelos
• por + as = pelas

Portuguese uses articles more often than English does.

So where English often says simply internet, Portuguese often says:

• a internet
• na internet
• pela internet

That is very normal.

This is one of the things English speakers need to get used to: Portuguese frequently uses definite articles with nouns where English would not.

Chegou is the preterite of chegar for ele/ela/você:

• chegar = to arrive
• chegou = arrived

The subject here is o pacote, which is singular, so the verb is singular too:

• O pacote chegou. = The package arrived.

The sentence has two past actions:

• eu pedi = I ordered
• o pacote chegou = the package arrived

Both are treated as completed events.

Because the sentence is built around the package as the main topic.

The basic structure is:

• O pacote ... chegou hoje de manhã.

Then que eu pedi pela internet is extra information describing o pacote.

So the sentence works like this:

• main subject: O pacote
• description of that subject: que eu pedi pela internet
• main verb: chegou
• time expression: hoje de manhã

This is very common in both Portuguese and English:

• The package that I ordered online arrived this morning.

Hoje de manhã means this morning or literally today in the morning.

It is a very common Brazilian Portuguese time expression:

• hoje de manhã = this morning
• hoje à tarde = this afternoon
• hoje à noite = tonight / this evening

Even though the literal pieces are:

• hoje = today
• de manhã = in the morning

the natural English translation is usually this morning.

Because de manhã is a fixed, very common time expression meaning in the morning / during the morning.

Examples:

• Eu estudo de manhã. = I study in the morning.
• Chegou hoje de manhã. = It arrived this morning.

Na manhã also exists, but it is used differently. It is usually more specific or more formal, as in:

• na manhã de segunda-feira = on Monday morning
• na manhã do dia 5 = on the morning of the 5th

So in everyday speech, hoje de manhã is the most natural choice.

Not in the same way.

In Portuguese, when you want to say the package that I ordered, you normally need the relative pronoun que:

• O pacote que eu pedi...

Saying O pacote eu pedi... would not mean the same thing naturally. It would sound like a different structure, more like a marked topic construction, and it would need a different context.

So for a normal descriptive sentence, que is the correct choice.

Yes, it is completely natural.

A Brazilian speaker might also say:

• O pacote que eu pedi na internet chegou hoje de manhã.
• O pacote que pedi pela internet chegou hoje de manhã.
• O pacote que eu comprei pela internet chegou hoje de manhã.
• O pacote chegou hoje de manhã. Eu pedi pela internet.

But your original sentence is normal, clear, and idiomatic.

A simple breakdown is:

• O pacote = the package
• que eu pedi pela internet = that I ordered online
• chegou = arrived
• hoje de manhã = this morning

So the full structure is:

• [Subject] O pacote
• [Relative clause] que eu pedi pela internet
• [Main verb] chegou
• [Time expression] hoje de manhã

That makes the whole sentence:

• The package that I ordered online arrived this morning.