Anotei o número da apólice.

Portuguese often leaves out the subject pronoun when the verb form already makes it clear who the subject is.
Here, anotei is the 1st person singular form, so it already means I wrote down / I noted down.

So:

• Anotei o número da apólice. = natural, normal
• Eu anotei o número da apólice. = also correct, but with extra emphasis, contrast, or clarity

This is very common in European Portuguese.

Anotei is the pretérito perfeito simples of anotar.

That means it describes a completed action in the past. In this sentence, the action of writing the number down is finished.

It is formed like this:

• infinitive: anotar
• verb stem: anot-
• eu ending in the preterite for -ar verbs: -ei
• result: anotei

So anotei = I wrote down / I noted down.

Anotar is a regular -ar verb, so it follows the normal pattern.

In the preterite:

• eu anotei
• tu anotaste
• ele/ela anotou
• nós anotámos
• vós anotastes
• eles/elas anotaram

So in your sentence, anotei is simply the regular eu form.

Because número is a masculine noun in Portuguese.

That means it takes masculine singular articles:

• o número
• not a número

This is something learners need to memorize with the noun. In Portuguese, noun gender does not always match English logic, but here the article tells you clearly that número is masculine.

Da is a contraction of:

• de
  • a = da

Here:

• a apólice = the policy
• o número da apólice = the number of the policy

Portuguese very often contracts de with the definite article:

• de + o = do
• de + a = da
• de + os = dos
• de + as = das

So da apólice is the normal and correct form.

Yes, apólice is a feminine noun, so it is:

• a apólice
• da apólice
• uma apólice

You can tell from the article used with it here: da contains a, the feminine singular article.

Also, this is a good reminder that noun gender in Portuguese is not always predictable from the ending. Even though apólice ends in -e, it is feminine, so it is best learned together with its article: a apólice.

Portuguese uses definite articles more often than English does.

In this sentence:

• o número refers to a specific number
• da apólice refers to a specific policy

Even if English might sometimes sound natural with fewer articles, Portuguese usually keeps them in this kind of structure.

So Anotei número da apólice would sound incomplete or unnatural in standard Portuguese.
Anotei o número da apólice is the normal form.

Sometimes yes, but the meaning and feel are slightly different.

• o número da apólice usually refers to the number of a specific policy
• o número de apólice is often more generic, like a label, category, or field on a form

For example:

• Anotei o número da apólice. = I wrote down the number of the policy
• Indique o número de apólice. = Enter policy number

So in your sentence, where someone is talking about one actual policy, da apólice is the more natural choice.

The accent marks show where the stress falls.

• número → stress on nú
• apólice → stress on pó

So the stressed syllables are:

• NÚ-me-ro
• a-PÓ-li-ce

These accents are important because they guide pronunciation and distinguish the normal stress pattern. Without them, a learner might stress the wrong syllable.

A simple learner-friendly approximation is:

ah-no-TEI u NU-muh-ru dah ah-PO-li-suh

A few helpful notes for European Portuguese:

• anotei ends with a sound like -tei
• o as an article is usually pronounced like u
• unstressed vowels are often reduced, especially in European Portuguese
• apólice has the stress on PÓ

So the strongest beats are:

anotei o NÚmero da aPÓlice

If you want to sound more natural, pay special attention to the stress rather than trying to pronounce every vowel as clearly as in English.