When to omit personal pronouns?

Question

In English a subject is almost always necessary to form a complete, natural sounding sentence. In Portuguese, it seems like one can choose to omit personal pronouns. For example, in the following sentences, the pronoun may be omitted.

[Eu] Vou comer alguma coisa.

[Nós] Moramos em São Paulo.

That's no problem, because everyone knows it's 1st person singular (resp. plural) because of the ending of the verb. But I don't exactly know when (if ever) it's better to include a pronoun. Is the version without pronoun considered informal? Does formal Portuguese always include the pronoun?

I also have a feeling that the first person pronoun is omitted much more often than the third person pronoun.

[Eles] Comem muito.

Is there a reason for that?

Answer 1

There is no difference in informality.

In Portugal, it is rather frequent to omit the pronoun.

The pronoun is not omitted if we wish to stress who we are talking about. In the example:

Onde vocês vão? - Eu vou comprar pão.

Here, I used ‘eu’ as a way of saying that I am speaking about myself. I don't know about what he/she/they are going to do.
If I had said ‘Vou comprar pão’, it could suggest he/she/they are coming with me.

We may also want to stress the meaning:

Por que é que ela não vem também? - Ela não quer.

Saying ‘Não quer’, would sound neutral, just informational.
Using the pronoun ‘ela’, I may stress either that it is her opinion, and should be respected, or that the first speaker already knows that she doesn't want to go and is useless to keep asking.

Adding the pronoun can also add certain levels of meaning:

Quem vem connosco? - Eu vou mais logo.

If the answer was ‘Vou mais logo’, it would sound as if the first speaker already knew I was going with them and I was just adding the information that I would meet with them later.

Another example. If I say:

Fizeste as compras?

... may sound neutral or surprised, depending on the intonation, but:

Tu fizeste as compras!?

... expresses that I could hardly imagine he or she would do the shopping. Normally, the pronoun would be stressed by the intonation.

In imperative constructions, as it happens in English, the second person pronoun is always omitted:

Faz o que te digo!

Answer 2

Is the version without pronoun considered informal? Does formal Portuguese always include the pronoun?

No, and sometimes omitting the pronoun can sound more formal than using it. It depends on the context, and the informal use varies from region to region. But I'd say that using the pronoun is so common in spoken language in every part of Brazil, that part of the verb inflections are in decline, as the pronoun already carries information of person and number. For example, this is very frequent:

Eu vou
Tu vai
Ele / você vai
Nós vai / nós vamo
--
Eles vai / vocês vai

Except for eu vou, these forms are not standard and should not be used in writing. In spoken language they're common, but also frowned upon as a sign of lack of formal instruction (which is not always true). See how there are only two or three forms of the verb left in the present indicative.

I also have a feeling that the first person pronoun is omitted much more often than the third person pronoun.

That sounds reasonable, but it might be because the third person is much more indefinite and context-sensitive. "Eu" is always clear in communication, it's the one emitting the speech. But "ele"/"eles" need further reference in the text/conversation to clarify who it refers to.