Niemowlę śpi spokojnie, kiedy przykrywam je miękkim kocykiem.

Polish does not have articles like English the and a/an.
So niemowlę can mean a baby or the baby, depending on context.

In this sentence, context usually makes it feel like the baby.

Niemowlę is a grammatically neuter noun in Polish. That is true even though it refers to a person.

Because it is neuter singular, the pronoun referring to it is je = it.

So:

• niemowlę = neuter noun
• je = accusative form referring back to that neuter noun

This is a good example of how grammatical gender in Polish does not always match natural gender.

Here is the case breakdown:

• niemowlę — nominative singular
  It is the subject of śpi.

• je — accusative singular
  It is the direct object of przykrywam.

• miękkim kocykiem — instrumental singular
  It shows what I am covering the baby with.

So the structure is basically:

• The baby sleeps...
• I cover it
• with a soft blanket

Because spokojnie is an adverb, and it describes how the baby sleeps.

• spokojny / spokojna / spokojne = adjective = calm, peaceful
• spokojnie = adverb = calmly, peacefully

Since it modifies the verb śpi (sleeps), Polish uses the adverb:

• śpi spokojnie = sleeps peacefully

Przykrywam is the imperfective present form of przykrywać.

That matters because in Polish:

• imperfective present can describe a real present action or a habitual action
• perfective “present” usually has future meaning

So:

• przykrywam = I am covering / I cover
• przykryję = I will cover

In this sentence, the action is happening in the present or is presented as a usual action, so przykrywam is the right choice.

Because Polish often uses the instrumental case after verbs like przykrywać / przykryć when you say what something is covered with.

The pattern is:

• przykrywać kogo? co? czym?
• to cover someone/something with something

So here:

• je = the thing/person being covered
• miękkim kocykiem = what it is covered with

Also, the adjective has to agree with the noun:

• kocyk — masculine singular
• instrumental singular: kocykiem
• matching adjective: miękkim

Kocyk is a diminutive of koc.

• koc = blanket
• kocyk = little blanket / baby blanket / cozy blanket

Diminutives are very common in Polish, especially when talking about children, babies, and soft or affectionate things.
So miękki kocyk sounds very natural here.

Kiedy basically means when.

In a sentence like this, with both verbs in the present tense, it can mean either:

• when — in a specific scene
• whenever — as a general repeated situation

So this sentence could be understood as:

• The baby sleeps peacefully when I cover it with a soft blanket
• or The baby sleeps peacefully whenever I cover it with a soft blanket

Context decides which meaning is stronger.

Because kiedy przykrywam je miękkim kocykiem is a subordinate clause.

In Polish, subordinate clauses are normally separated by a comma.
So the comma before kiedy is required.

You would also keep a comma if the clause came first:

• Kiedy przykrywam je miękkim kocykiem, niemowlę śpi spokojnie.

Yes. Polish word order is more flexible than English word order.

For example, you can also say:

• Kiedy przykrywam je miękkim kocykiem, niemowlę śpi spokojnie.

This means basically the same thing, but the focus shifts a little. Starting with kiedy... puts more emphasis on the time/situation.

However, some parts still tend to stay together naturally:

• śpi spokojnie
• przykrywam je
• miękkim kocykiem

So Polish is flexible, but not random.

Usually no, not in this sentence.

Przykrywam normally needs an object: I cover whom/what?
So je is doing important work here.

If you said only:

• kiedy przykrywam miękkim kocykiem

it would sound incomplete, because the listener expects to hear what is being covered.

So keeping je is the natural choice.

No. Je can have more than one use in Polish.

It can mean:

• it — for a neuter singular noun
• them — for some plural nouns, depending on gender

But in this sentence it clearly means it, because it refers back to the singular neuter noun niemowlę.