O desalfandegamento demorou dois dias.

O is the masculine singular definite article, meaning the.

It is used because desalfandegamento is a masculine singular noun:

• o desalfandegamento
• os desalfandegamentos

So the sentence begins literally as The customs clearance...

They are related, but they do not mean the same thing.

• alfândega = customs (the customs office / customs authority)
• desalfandegamento = customs clearance (the process of clearing goods through customs)

So:

• A encomenda está na alfândega. = The parcel is at customs.
• O desalfandegamento demorou dois dias. = The customs clearance took two days.

Desalfandegamento is a more technical/process-based noun.

It is a real and correct word, but it sounds a bit formal, technical, or logistics/customs-related.

In everyday conversation, people might sometimes say things like:

• ficou na alfândega = it got held at customs
• o processo na alfândega = the process at customs
• o desembaraço aduaneiro = customs clearance (also formal/technical)

So desalfandegamento is perfectly fine, especially in shipping, legal, or administrative contexts.

Demorou is the preterite (simple past) of demorar.

Here it means:

• took
• lasted
• required this amount of time

So:

• demorou dois dias = took two days

Examples:

• A viagem demorou três horas. = The trip took three hours.
• O processo demorou muito. = The process took a long time.

In Portuguese, with demorar, you usually do not need a preposition equivalent to English for in this structure.

English:

• It took two days
• It lasted for two days

Portuguese:

• Demorou dois dias

So dois dias is a direct expression of duration.

More examples:

• A reunião demorou uma hora.
• A obra demorou seis meses.

This is very normal Portuguese.

Because the subject is O desalfandegamento, which is singular.

Structure:

• O desalfandegamento = subject
• demorou = singular verb
• dois dias = duration

Even though dois dias is plural, it is not the subject. It tells you how long the process took.

So the agreement is with desalfandegamento, not with dois dias.

Yes. Levou dois dias is also very natural.

Compare:

• O desalfandegamento demorou dois dias.
• O desalfandegamento levou dois dias.

Both can mean The customs clearance took two days.

A small nuance:

• demorar focuses on duration / taking time
• levar in this kind of sentence also means to take (time) and is very common

Both are correct and natural.

Yes, the given order is the most neutral and standard:

• O desalfandegamento demorou dois dias.

But Portuguese allows some flexibility. You could also say:

• Demorou dois dias, o desalfandegamento.
  This is possible, but marked and less neutral.
• Foram dois dias de desalfandegamento.
  This changes the structure slightly.

For a learner, the safest default is: subject + verb + duration

A rough guide is:

de-zal-fan-de-ga-MEN-tu

A few notes for European Portuguese:

• The stress falls on -men-: desalfandegaMENto
• The final -o is often reduced, sounding closer to u
• Unstressed vowels may sound weaker than in English

You may also notice that European Portuguese tends to compress unstressed syllables more than Brazilian Portuguese.

Yes. The ending -mento is a very common noun-forming suffix in Portuguese, often like English -ment or -ing/process nouns.

Examples:

• pagamento = payment
• nascimento = birth
• funcionamento = functioning / operation
• desalfandegamento = customs clearance

So desalfandegamento is basically the process/result noun built from a related verbal idea.

Because dias is a masculine plural noun.

• singular: o dia
• plural: os dias

So the numeral must match:

• dois dias
• duas semanas

Even though some learners expect day to be feminine because of associations from other languages, in Portuguese dia is usually masculine.

Normally, no. In standard Portuguese, you would usually keep the article here:

• O desalfandegamento demorou dois dias.

Without o, it sounds incomplete or unnatural in most normal contexts.

Portuguese often uses the definite article more than English does with concrete or specific nouns. Since we are talking about a particular customs-clearance process, o is the natural choice.

Not in the same way.

• demorou dois dias = it took two days
• por dois dias usually means for two days in the sense of throughout a two-day period

So:

• O desalfandegamento demorou dois dias. = The customs clearance took two days.
• Ficou retido na alfândega por dois dias. = It was held at customs for two days.

With demorar, the normal pattern is simply:

• demorar + period of time

Yes, it works in European Portuguese, and it would also be understood in other varieties of Portuguese.

What makes it suitable for Portugal is mainly:

• the vocabulary is valid in Portugal
• the sentence structure is standard
• alfândega and desalfandegamento are normal words in Portuguese used in Portugal

That said, usage frequency may vary by region, and in informal speech people may prefer less technical wording.