Depois do banho, eu coloco a bebê no berço e cubro as pernas dela.

Because depois normally takes de before a noun: depois de + noun.

So:

• depois de o banho is the full form
• de + o contracts to do
• therefore: depois do banho

This kind of contraction is very common in Portuguese:

• de + a = da
• em + o = no
• em + a = na

By itself, it could technically be either. Portuguese leaves that to context, just like English sometimes does.

In this sentence, because the speaker then puts the baby in the crib and covers her legs, the most natural interpretation is after the baby's bath or after bath time.

If you wanted to make it extra clear, you could say depois do banho dela.

Because depois do banho is an introductory time expression placed at the beginning of the sentence.

In Portuguese, it is very common to separate that kind of opening phrase with a comma:

• Depois do banho, eu coloco...
• De manhã, eu estudo.
• À noite, eles saem.

In informal writing, very short opening phrases are sometimes written without a comma, but here the comma is natural and standard.

Not always. Portuguese often drops subject pronouns when the verb already makes the subject clear.

So both of these are natural:

• Depois do banho, eu coloco a bebê no berço...
• Depois do banho, coloco a bebê no berço...

Using eu can add a little emphasis, contrast, or clarity, but it is not required.

Coloco is the present indicative of colocar.

Here it describes a routine or habitual action:

• Depois do banho, eu coloco... = After the bath, I put... / I place...

Portuguese often uses the simple present for things someone regularly does, just like English can:

• I brush my teeth at night.
• Eu escovo os dentes à noite.

Bebê can be either masculine or feminine depending on the article and the person being referred to.

• o bebê = the baby boy / the baby
• a bebê = the baby girl

In this sentence, a bebê tells you the baby is female.

Also, Portuguese usually wants an article or another determiner with a singular count noun in a sentence like this, so coloco bebê no berço would not sound right in normal usage.

Because with colocar, Portuguese normally uses em to say where something is being placed.

So:

• colocar no berço
• colocar na cama
• colocar na cadeira

Here, em + o berço contracts to no berço.

Using ao berço would not be the normal choice with colocar.

Because the verb here is cobrir (to cover), and its first-person singular form is cubro.

Examples:

• eu cubro
• você cobre
• eles cobrem

Cobro is from a different verb, cobrar, which usually means to charge, to collect, or to demand.

So:

• eu cubro as pernas = I cover the legs
• eu cobro = I charge / I collect

Both are possible, but as pernas dela is clearer.

That is because seu/sua/seus/suas can be ambiguous in Portuguese. Depending on context, suas pernas could mean:

• her legs
• his legs
• your legs
• sometimes even their legs

Using dela removes the ambiguity:

• as pernas dela = her legs

So this sentence chooses the clearer option.

Dela literally comes from de + ela and means of her or hers depending on context.

In as pernas dela, it works like a possessive:

• as pernas dela = her legs
  literally: the legs of her

This structure is very common in Portuguese:

• o carro dele = his car
• a bolsa dela = her bag
• os brinquedos deles = their toys

Yes. Pôr and colocar can both mean to put.

So these are both possible:

• eu coloco a bebê no berço
• eu ponho a bebê no berço

However, colocar is often easier for learners because it is more regular in its forms:

• coloco, coloca, colocamos

Pôr is very common too, but it is more irregular:

• ponho, põe, pomos
• past forms like pus

So the sentence uses a very natural and learner-friendly verb choice.