Ela colocou a mão no ombro da filha e sorriu.

Both are in the pretérito perfeito, the tense usually used for completed actions in the past.

• ela colocou = she put / placed
• (ela) sorriu = she smiled

In this sentence, the two actions happen as finished events in sequence:

1. she put her hand on her daughter’s shoulder
2. she smiled

Portuguese very often uses the definite article with body parts, especially when the owner is already clear from the context.

So:

• colocou a mão literally = put the hand
• but naturally it means = put her hand

In English, we usually prefer the possessive: her hand. In Portuguese, that would often sound less natural here unless you need extra emphasis or clarification.

No is a contraction of:

• em + o = no

So:

• no ombro = literally in/on the shoulder

Even though em often means in, Portuguese uses it in many places where English uses on. In this sentence, no ombro is best understood as:

• on the shoulder

So colocou a mão no ombro = put her hand on the shoulder

Because ombro is a masculine noun.

• o ombro = the shoulder
• em + o ombro = no ombro

If the noun were feminine, you would get na:

• em + a = na

So the form of the contraction depends on the gender of the noun.

Da is a contraction of:

• de + a = da

So:

• o ombro da filha = literally the shoulder of the daughter

In natural English, this is usually:

• the daughter’s shoulder
• or, in context, her daughter’s shoulder

Here, da filha tells us whose shoulder it is.

The most natural reading is:

• her own hand
• her daughter

So the sentence is normally understood as: She put her hand on her daughter’s shoulder and smiled.

Portuguese often leaves this kind of possession implicit when it is obvious from context, especially with:

• body parts
• family relationships
• close personal reference

Because Portuguese often drops subject pronouns when the subject is already clear. This is very common.

So instead of saying:

• Ela colocou a mão no ombro da filha e ela sorriu

Portuguese normally says:

• Ela colocou a mão no ombro da filha e sorriu

The subject of sorriu is still understood to be ela.

By itself, sorriu just means smiled.

If Portuguese wants to say exactly smiled at her daughter, it can say:

• sorriu para a filha

In your sentence, the person she smiled at is not stated explicitly, but the context may strongly suggest it was the daughter.

So the sentence simply gives the action:

• she smiled

and lets the reader infer more from the situation.

Yes. A very natural alternative is:

• Ela pôs a mão no ombro da filha e sorriu.

Both colocar and pôr can mean to put / to place.

A rough comparison:

• colocar = a bit more neutral or slightly more formal
• pôr = very common and everyday

In Brazilian Portuguese, both are perfectly natural here.

Yes, it sounds very natural.

It has several features that are typical of normal Portuguese:

• definite article with a body part: a mão
• contractions: no, da
• omitted repeated subject: e sorriu

It also sounds like a very normal narrative sentence describing a gentle or affectionate action.