Moje kapcie stoją przy łóżku, a szlafrok wisi na drzwiach łazienki.

Because kapcie is a plural non-masculine noun, so it takes the possessive form moje.

A quick comparison:

• mój = for singular masculine nouns
• moja = for singular feminine nouns
• moje = for singular neuter nouns and for plural non-masculine nouns
• moi = for plural masculine-personal nouns

So:

• mój szlafrok = my bathrobe
• moja książka = my book
• moje łóżko = my bed
• moje kapcie = my slippers

You use moi only with groups of male people or mixed-person groups, for example moi koledzy.

In this sentence, kapcie is plural and means slippers.

In everyday Polish, kapcie is very commonly used for a pair of house slippers. A learner may notice that Polish often talks about items like this in the plural, just like English says slippers rather than usually a slipper when talking about the pair.

So:

• kapcie stoją = the slippers are standing / are by the bed

Polish very often uses specific position verbs where English would simply say is/are.

Here, stać / stoją means something like:

• to stand
• to be standing
• to be upright / placed somewhere

For many objects, Polish prefers this kind of verb if the position is natural or visible.

So:

• kapcie stoją przy łóżku literally = the slippers are standing by the bed
• natural English = the slippers are by the bed

It may sound odd in English, but in Polish it is completely normal.

For the same reason: Polish often uses a position or posture verb instead of a general to be.

• wisi = is hanging
• from wisieć = to hang

So szlafrok wisi na drzwiach łazienki literally means:

• the bathrobe is hanging on the bathroom door

This is very natural Polish. The language often prefers:

• stoi = is standing
• leży = is lying
• wisi = is hanging

instead of a basic is.

They use different prepositions because the location is different.

• przy łóżku = by / next to the bed
• na drzwiach = on the door

So:

• przy means near, by, next to
• na means on

Both of these prepositions require the locative case here, which is why the nouns change form:

• łóżko → łóżku
• drzwi → drzwiach

Because after przy, Polish uses the locative case.

The dictionary form is:

• łóżko = bed

After przy, it changes to:

• przy łóżku = by the bed

This is a standard case change. Many Polish prepositions force a particular case, and learners need to memorize which case goes with which preposition.

Because na here also takes the locative case, so drzwi changes to drzwiach.

• dictionary form: drzwi = door / doors
• locative form: drzwiach

So:

• na drzwiach = on the door

This form is especially worth noticing because drzwi is a special noun in Polish.

Because drzwi is a plural-only noun in Polish. Grammatically, it behaves like a plural noun even when it refers to one door.

That is why you get plural-looking forms such as:

• te drzwi = this door / these doors
• na drzwiach = on the door
• drzwi są otwarte = the door is open

This feels strange to English speakers at first, but it is normal in Polish.

Because łazienki here means of the bathroom, not in the bathroom.

The phrase is:

• drzwi łazienki = the bathroom door
  literally: the door of the bathroom

After one noun modifies another like this, Polish often uses the genitive case for the second noun:

• łazienka = bathroom
• łazienki = of the bathroom

If you said w łazience, that would mean in the bathroom, which is a different idea.

In this sentence, a links two facts, but with a slight sense of contrast or separate focus.

• i = and
• a = and / while / whereas, depending on context

So:

• Moje kapcie stoją przy łóżku, a szlafrok wisi na drzwiach łazienki.

means something like:

• My slippers are by the bed, and my bathrobe is hanging on the bathroom door
• or slightly more literally: My slippers are by the bed, while the bathrobe is hanging on the bathroom door

Using a sounds natural because it presents two different items in two different places.

Sometimes yes, but it would usually sound less natural or less specific.

For example:

• Kapcie są przy łóżku = The slippers are by the bed
• Szlafrok jest na drzwiach łazienki = The bathrobe is on the bathroom door

These are understandable, but Polish often prefers the more descriptive verbs:

• stoją for something standing
• wisi for something hanging

So the original sentence sounds more natural and vivid.

No, Polish word order is quite flexible, though some versions sound more natural than others.

The original:

• Moje kapcie stoją przy łóżku, a szlafrok wisi na drzwiach łazienki.

is neutral and natural.

You could change the order for emphasis, for example:

• Przy łóżku stoją moje kapcie... = By the bed are my slippers...
• Na drzwiach łazienki wisi szlafrok. = On the bathroom door hangs a bathrobe.

But these versions shift the emphasis. For a learner, the original order is the safest and most natural.

A rough pronunciation guide is:

• Moje ≈ MO-ye
• kapcie ≈ KAP-chye
• stoją ≈ STO-yow̃
• przy ≈ pshih
• łóżku ≈ WOOSH-koo
• a ≈ ah
• szlafrok ≈ SHLAF-rok
• wisi ≈ VEE-shee
• na ≈ nah
• drzwiach ≈ roughly דזשvyahkh / jvyahh (this cluster is hard for beginners)
• łazienki ≈ wa-ZYEN-kee

A few useful pronunciation points:

• ł sounds like English w
• sz sounds like sh
• ci before a vowel often sounds like a soft ch / ć
• rz / ż sounds like the s in measure
• ą is a nasal vowel

Yes. That is a very common alternative.

• przy łóżku = by the bed, right near it
• obok łóżka = next to the bed / beside the bed

Both are natural, but the nuance is slightly different:

• przy often suggests close proximity
• obok clearly means next to / beside

Notice the case difference too:

• przy łóżku → locative
• obok łóżka → genitive

So this is a good example of how changing the preposition can also change the case.

They are:

Nouns:

• kapcie = slippers
• łóżko = bed
• szlafrok = bathrobe / dressing gown
• drzwi = door
• łazienka = bathroom

Verbs:

• stać = to stand
• wisieć = to hang

Forms used in the sentence:

• stoją = they stand / are standing
• wisi = it hangs / is hanging

Learning both the dictionary form and the sentence form is very useful, because Polish changes words a lot depending on case, number, and person.