Peškir je u kupatilu, a sapun je blizu ogledala.

Je is the 3rd person singular present form of biti (to be) — in other words, is.

The sentence has two separate clauses:

• Peškir je u kupatilu
• a sapun je blizu ogledala

Each clause has its own subject and its own je, so repeating it is completely normal.

A often translates as and, but it is not exactly the same as English and in every situation.

Here, a links two ideas while also slightly contrasting or shifting attention:

• The towel is in the bathroom, and/as for the soap, it is near the mirror.

So a is very common when Serbian moves from one topic to another. It is weaker than ali (but), but it can still suggest a mild contrast.

Because u changes case depending on meaning.

• u + locative = in/inside a place, with no movement
• u + accusative = into a place, showing movement

Here the towel is already located in the bathroom, so Serbian uses the locative:

• kupatilo → kupatilu

Compare:

• Peškir je u kupatilu = The towel is in the bathroom.
• Stavljam peškir u kupatilo = I am putting the towel into the bathroom.

Because blizu is followed by the genitive case.

The base form is:

• ogledalo = mirror

But after blizu, it becomes genitive singular:

• blizu ogledala = near the mirror

This is something you mostly have to learn with the word blizu: it regularly governs the genitive.

It is genitive singular.

The noun is:

• ogledalo = nominative singular

After blizu, it changes to:

• ogledala = genitive singular

This is a very common pattern in Serbian: certain prepositions and preposition-like words require specific cases.

Here are the genders:

• peškir = masculine
• sapun = masculine
• kupatilo = neuter
• ogledalo = neuter

Useful general rule:

• nouns ending in a consonant are often masculine
• nouns ending in -o or -e are often neuter
• nouns ending in -a are often feminine

This is only a general guide, but it works well for these words.

Because Serbian does not have articles like English a/an and the.

So:

• peškir can mean a towel or the towel
• sapun can mean a soap bar / soap or the soap

The exact meaning depends on context. Serbian speakers understand from the situation what is meant.

No, Serbian word order is fairly flexible, but not completely random.

The version you have is a natural, neutral order:

• Peškir je u kupatilu, a sapun je blizu ogledala.

You could also say:

• U kupatilu je peškir, a blizu ogledala je sapun.

That changes the emphasis a little, focusing more on the locations.

One important detail: je is a clitic, so it usually appears near the beginning of its clause, often in the second position. That is why Peškir je... sounds natural.

Peškir is pronounced approximately like PESH-keer.

The most important letter here is:

• š = English sh

So:

• peš- sounds like pesh-

Also, Serbian spelling is very phonetic, so words are usually pronounced much more closely to how they are written than in English.

In learner terms, it is easiest to treat blizu as a word meaning near/close to that is followed by the genitive.

So in practice:

• blizu ogledala = near the mirror
• blizu kuće = near the house
• blizu škole = near the school

Whether grammar books classify it as a preposition or a preposition-like adverb, the key thing for a learner is this: the noun after it goes into the genitive.