Proszek do prania leży obok pralki w łazience.

Because obok normally requires the genitive case.

• dictionary form: pralka = washing machine
• after obok: obok pralki = next to the washing machine

This is very common in Polish:

• obok stołu = next to the table
• obok domu = next to the house
• obok pralki = next to the washing machine

So the ending changes because the preposition controls the case.

Because w meaning in usually takes the locative case when talking about location.

• dictionary form: łazienka = bathroom
• locative singular: łazience
• so: w łazience = in the bathroom

This is the normal pattern for location:

• w domu = in the house
• w szkole = at school / in the school
• w łazience = in the bathroom

So both pralki and łazience are case forms caused by prepositions.

Leży literally means is lying or lies, and Polish often uses verbs of position where English would simply say is.

So:

• Proszek do prania jest obok pralki would be understandable
• but Proszek do prania leży obok pralki sounds more natural if the item is physically lying somewhere

It suggests the detergent is placed there as an object, not just existing there.

Polish often does this with position verbs:

• książka leży na stole = the book is lying on the table
• krzesło stoi przy ścianie = the chair is standing by the wall
• obraz wisi na ścianie = the picture is hanging on the wall

English often just uses is, but Polish prefers a more specific verb.

This is a very common Polish pattern: noun + do + genitive to mean for / used for something.

So:

• proszek = powder
• pranie = washing / laundry
• do prania = for washing

Together, proszek do prania literally means powder for washing, which is the standard way to say laundry detergent / washing powder.

You can compare:

• szczotka do zębów = toothbrush
• pasta do zębów = toothpaste
• maszyna do szycia = sewing machine

So do here does not mean movement toward something. It means for the purpose of.

Because do requires the genitive case.

The noun is pranie. After do, it becomes prania:

• pranie → do prania

This is the same kind of pattern as:

• do domu = to the house / home
• do szkoły = to school
• do kawy = for coffee / to coffee

So in this sentence, there are two genitives:

• do prania
• obok pralki

In everyday Polish, proszek do prania usually means washing powder, but speakers may also use it in a broader household sense when talking about laundry detergent.

Still, if you want to be precise:

• proszek do prania = washing powder
• płyn do prania = liquid laundry detergent

So the phrase is quite literal, but in casual use people may not always be very technical about the product type.

Yes. Polish word order is relatively flexible, because case endings show the relationships between words.

The neutral order here is:

• Proszek do prania leży obok pralki w łazience.

But you could also say:

• W łazience proszek do prania leży obok pralki.
• Obok pralki w łazience leży proszek do prania.

These all mean basically the same thing, but the emphasis changes:

• sentence-initial W łazience emphasizes the place
• sentence-initial Obok pralki emphasizes the exact position
• the original version is a normal, neutral statement

In normal interpretation, it describes the location of the whole scene: the detergent is next to the washing machine, and this is happening in the bathroom.

So the natural reading is:

• the detergent is next to the washing machine
• the washing machine is in the bathroom
• the detergent is therefore in the bathroom too

Polish allows this kind of compact phrasing, just like English does in The detergent is next to the washing machine in the bathroom.

If context mattered, a speaker could rephrase to make it clearer, but this sentence is perfectly natural as it stands.

Leży is the 3rd person singular present tense form of the verb leżeć.

The subject is proszek do prania, which is grammatically singular, so the verb must also be singular:

• ja leżę = I am lying
• ty leżysz = you are lying
• on/ona/ono leży = he/she/it is lying

Here the subject is an inanimate noun phrase, so Polish uses the same form as he/she/it:

• proszek do prania leży

Because Polish has no articles like English a/an/the.

So:

• pralka can mean a washing machine or the washing machine
• łazienka can mean a bathroom or the bathroom

The exact meaning depends on context.

In this sentence, English naturally uses the in translation, but Polish does not need any article at all.

Yes. Koło pralki is also very common and natural.

Both can mean next to / beside:

• obok pralki
• koło pralki

In many everyday situations, they are interchangeable. A learner will hear both. Like obok, koło also takes the genitive:

• koło stołu
• koło domu
• koło pralki

So if you already know one of them, the other is worth learning as a very common alternative.