Kuweta stoi w łazience obok pralki, dlatego kot zawsze wie, gdzie iść.

Because w means in here, and when w describes a location, Polish normally uses the locative case.

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

So:

• łazienka = the bathroom
• w łazience = in the bathroom

This kind of change is very common in Polish.

Because the preposition obok (next to / beside) requires the genitive case.

• dictionary form: pralka = washing machine
• genitive singular: pralki

So:

• obok pralki = next to the washing machine

This is something you often just have to learn with the preposition:

• w
  • locative for location
• obok
  • genitive

In Polish, it is very natural to use verbs like:

• stać = to stand
• leżeć = to lie
• wisieć = to hang

for the position of objects.

So Kuweta stoi w łazience sounds natural and means the litter box is standing / placed in the bathroom.

You could also say Kuweta jest w łazience, which simply means The litter box is in the bathroom, but stoi sounds more idiomatic for a physical object located somewhere.

Dlatego means therefore, that’s why, or for that reason.

It connects the two parts like this:

• the litter box is in the bathroom next to the washing machine
• therefore / that’s why the cat always knows where to go

So it introduces the result of the first clause.

Because the sentence contains two separate clauses:

• Kuweta stoi w łazience obok pralki
• dlatego kot zawsze wie, gdzie iść

In Polish, when clauses like this are joined with a linking word such as dlatego, a comma is normally used.

So the comma is standard punctuation here.

These two structures mean different things.

• wie, gdzie iść = knows where to go
• wie, gdzie idzie = knows where he/it is going

In your sentence, the idea is that the cat knows the correct destination. That is why Polish uses gdzie iść with the infinitive.

A useful pattern is:

• wiem, co zrobić = I know what to do
• wie, gdzie iść = he/it knows where to go

Because iść and chodzić are not interchangeable.

• iść = to go, in one direction, on a particular occasion
• chodzić = to go/walk around habitually, repeatedly, or in general

Here the cat knows where to go in a specific sense: where it should go when it needs to use the litter box. So iść is the natural choice.

If you used chodzić, it would sound more like a general or repeated activity, not the destination-focused idea in this sentence.

This is a very common learner question.

Strictly speaking:

• gdzie = where
• dokąd = where to

But in everyday Polish, gdzie is very often used with verbs of motion where English would say where to.

So:

• wie, gdzie iść is completely natural
• wie, dokąd iść is also possible and a bit more explicitly directional

In normal speech, gdzie iść is very common.

Kot is in the nominative singular, because it is the subject of the second clause.

• kot = the cat
• kot zawsze wie = the cat always knows

So the basic structure is:

• subject: kot
• adverb: zawsze
• verb: wie

Here is a quick breakdown:

• kuweta — feminine, nominative singular
  It is the subject of the first clause.

• łazience — locative singular of łazienka
  Used after w to show location.

• pralki — genitive singular of pralka
  Used after obok.

• kot — masculine animate, nominative singular
  It is the subject of the second clause.

This sentence is a good example of how Polish changes noun endings depending on grammar and prepositions.

No. Polish usually does not use subject pronouns unless they are needed for emphasis or contrast.

Since the sentence already has kot, there is no reason to add on.

So:

• kot zawsze wie = natural
• on zawsze wie = possible only if you specifically want to stress he/it

Polish generally uses fewer subject pronouns than English.

Not completely. Polish word order is more flexible than English, because cases show grammatical relationships.

The version you have is very natural and neutral:

• Kuweta stoi w łazience obok pralki, dlatego kot zawsze wie, gdzie iść.

But you could change the order for emphasis, for example:

• W łazience obok pralki stoi kuweta...
  This puts more focus on the location.

The second clause is also fairly flexible, but kot zawsze wie is one of the most natural orders.

Because that is a very natural place for an adverb in Polish.

• kot zawsze wie = the cat always knows

Polish adverb placement is somewhat flexible, but:

• kot zawsze wie sounds neutral and natural
• kot wie zawsze is much less natural in an ordinary sentence and would usually need special emphasis

So this placement is the standard, everyday choice.