Gdy wracam do domu, zakładam kapcie i ciepły szlafrok.

Here gdy means when.

In this sentence, gdy wracam do domu = when I come back home / when I get home.

For many learners, gdy and kiedy seem interchangeable, and very often they are. Both can mean when.
A small difference is that gdy can sound a bit more neutral or slightly more formal/literary in some contexts, while kiedy is very common in everyday speech.

So you could also say:

Kiedy wracam do domu, zakładam kapcie i ciepły szlafrok.

and it would still sound natural.

In Polish, the present tense is commonly used for habitual actions, just like in English:

• When I get home, I put on slippers...
• Whenever I come home, I put on slippers...

So wracam literally means I am returning / I return, but in this kind of sentence it means something like when I come back or when I get home as a regular action.

This is completely normal Polish usage.

Because Polish usually does not need subject pronouns like ja when the verb already shows who is doing the action.

• wracam = I return / I’m coming back
• zakładam = I put on

The ending -am already tells you it is I.

You can add ja for emphasis, but normally it is omitted:

• Ja wracam do domu... = I am the one who comes home...

Without emphasis, leaving it out is more natural.

Because after do meaning to or into, Polish uses the genitive case.

So:

• dom = house / home
• do domu = to home / homeward

This is the normal expression for going/coming home:

• iść do domu = to go home
• wracać do domu = to return home

So wracam do domu is the standard way to say I’m coming back home.

Yes. Here zakładam means I put on.

The verb zakładać / założyć can mean to put on clothes, shoes, glasses, etc.

Examples:

• zakładać buty = to put on shoes
• zakładać płaszcz = to put on a coat
• zakładać okulary = to put on glasses

In your sentence:

• zakładam kapcie = I put on slippers
• zakładam ciepły szlafrok = I put on a warm bathrobe

This verb has other meanings in other contexts too, but here it clearly means put on clothing.

Yes. Kapcie is the plural form and means slippers.

The singular form is:

• kapeć = slipper

But in real life, people usually talk about slippers in the plural, because you normally wear a pair:

• zakładam kapcie = I put on slippers

This is very similar to English, where slippers is also usually plural.

Because szlafrok is a masculine inanimate noun, and in this sentence it is the direct object of zakładam.

For masculine inanimate nouns, the accusative is the same as the nominative.

So:

• ciepły szlafrok = nominative
• zakładam ciepły szlafrok = accusative, but it looks the same

That is why the adjective also stays:

• ciepły, not ciepłego

Compare that with a masculine animate noun, where the accusative changes:

• widzę dobrego psa = I see a good dog

But:

• zakładam ciepły szlafrok = I put on a warm bathrobe

Because Polish, like English, does not need to repeat the verb or structure when one verb applies to two objects.

So:

zakładam kapcie i ciepły szlafrok

means:

I put on slippers and a warm bathrobe.

You could repeat things for emphasis or clarity, but normally you would not:

• zakładam kapcie i zakładam ciepły szlafrok — grammatical, but unnecessary and unnatural in this context

The shorter version is the natural one.

No, Polish word order is fairly flexible, although some orders sound more natural than others.

The given sentence is very natural:

Gdy wracam do domu, zakładam kapcie i ciepły szlafrok.

You could also say:

• Zakładam kapcie i ciepły szlafrok, gdy wracam do domu.

This is still correct, but it places the focus a bit differently.

The original version is probably the most neutral and natural if you are simply describing a routine:
When I come home, I put on slippers and a warm bathrobe.

Yes, szlafrok is a normal Polish word. It means bathrobe, robe, or dressing gown.

So:

• ciepły szlafrok = a warm bathrobe / dressing gown

A native English speaker may wonder whether this sounds old-fashioned. In Polish, szlafrok is a standard everyday word.

Yes, in everyday Polish you can often say:

Jak wracam do domu, zakładam kapcie i ciepły szlafrok.

Here jak can mean when / whenever in conversational speech.

However:

• gdy is more neutral/written
• kiedy is very common and standard
• jak is more colloquial in this meaning

So all three may be possible depending on style, but gdy and kiedy are usually safer for learners.

A rough English-style pronunciation would be:

gdi vra-tsam do DOH-moo, za-KWA-dam KAP-chye ee CHYE-pwi SHLAF-rok

A few important sounds:

• gdy: the gd cluster is tricky; it sounds roughly like gdi
• wracam: w sounds like English v
• cz in kapcie sounds like ch
• cie in ciepły sounds roughly like chye
• sz in szlafrok sounds like English sh
• ł in ciepły sounds like English w

This is only an approximation, but it can help you get started.