W torbie mam czystą pieluchę, bo dziś wracamy do domu późno.

Because the preposition w meaning in usually takes the locative case when it describes location.

• torba = bag
• w torbie = in the bag

So torbie is the locative singular form of torba.

Mam means I have. It is the 1st person singular form of mieć (to have).

So:

• mam = I have

In this sentence, the speaker is saying that they have a clean diaper in the bag.

Polish often leaves out subject pronouns because the verb ending already shows who is doing the action.

• mam already means I have
• wracamy already means we are returning / we return

So ja and my are not necessary unless you want extra emphasis.

Because mam takes a direct object, and the direct object here is in the accusative case.

The base form is:

• czysta pielucha = a clean diaper

But after mam, it changes to accusative:

• czystą pieluchę

Both the adjective and the noun change because they agree with each other.

For feminine singular nouns like pielucha, the accusative forms are often:

• -a → -ę for the noun
• -a → -ą for the adjective

Pielucha means diaper in American English or nappy in British English.

In everyday context, this sentence strongly suggests the speaker is out with a baby or small child.

Usually it means a clean/fresh diaper, and in real-life context that often implies unused.

So even though czysty literally means clean, here it naturally sounds like a fresh diaper to change the baby into.

Bo means because.

It is very common in everyday spoken and written Polish. It sounds natural and neutral in a sentence like this.

You could also use ponieważ, which also means because, but bo is more common in casual everyday speech.

Polish often uses the present tense to talk about a planned or expected future action, especially when the time is clear from context.

So:

• dziś wracamy do domu późno literally looks like today we return home late
• but in natural English it often means we’re coming home late today or we’ll get home late today

This is a very normal use of the present tense in Polish.

Because the preposition do takes the genitive case.

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

In Polish, wracać do domu is the normal way to say to return home.

Polish dom can mean both house and home, depending on context.

In the phrase wracać do domu, it usually means to go back home rather than specifically to the physical house.

So do domu is a very standard way to say home in this kind of sentence.

Późno means late, and here it is an adverb because it describes how/when we are returning.

• późno = late
• późny / późna / późne = late, but as an adjective

In this sentence, we need the adverb:

• wracamy późno = we’re coming back late

Not the adjective.

Dziś means today.

It gives the time reference for wracamy:

• dziś wracamy do domu późno = today we’re coming home late

You can also say dzisiaj. Both mean today.
Dziś is just a shorter form.

No, Polish word order is fairly flexible.

The given sentence:

• W torbie mam czystą pieluchę, bo dziś wracamy do domu późno.

sounds natural and puts a little emphasis on w torbie (in the bag).

You could also say:

• Mam w torbie czystą pieluchę, bo dziś wracamy do domu późno.

That also sounds natural. The meaning stays basically the same, but the emphasis shifts slightly.

Not if you want to keep the same meaning.

• W torbie mam czystą pieluchę = I have a clean diaper in the bag
• W torbie jest czysta pielucha = There is a clean diaper in the bag

So mam focuses on the speaker possessing/carrying it, while jest would simply state that it is there.