Tvoj kaput je ispod stolice, a moj je iznad torbe na polici.

Because Serbian often leaves out a noun if it is already obvious from context. In the second clause, moj means my one / mine, with kaput understood.

So:

• Tvoj kaput = your coat
• moj = my coat / mine

Grammatically, moj is still matching the omitted noun kaput, so it stays masculine singular nominative. If the omitted noun were feminine, the form would change:

• Moja je ispod stola. = Mine is under the table (with a feminine noun understood, like torba)

There are really two clauses here:

• Tvoj kaput je ispod stolice
• a moj je iznad torbe na polici

Each clause has its own je (is), so repeating it is normal.

Also, je is a clitic in Serbian. Clitics usually go in the second position of their clause. That is why you get:

• moj je
• not je moj

You may sometimes hear the second je left out in casual speech if the meaning is clear, but the full version with je is standard and very natural.

Here a links two parallel statements and adds a mild contrast or comparison.

In English, depending on context, it can sound like:

• and
• while
• whereas
• sometimes even a light but

In this sentence, a works well because the speaker is comparing your coat and my coat. It is softer than ali, which is a stronger but.

Because the prepositions ispod (under/below) and iznad (above) require the genitive case.

So:

• stolica → stolice
• torba → torbe

That gives:

• ispod stolice
• iznad torbe

This is something you have to learn together with the preposition:
ispod + genitive, iznad + genitive.

Because the prepositions tell you what case must follow.

Since ispod and iznad require genitive, the forms after them are understood as genitive. Context also helps:

• ispod stolice naturally means under the chair
• iznad torbe naturally means above the bag

It is true that forms like stolice and torbe can look identical to other forms in Serbian, so learners often have to rely on:

1. the preposition,
2. the case rule,
3. the context.

Because na can take different cases depending on whether you mean location or movement.

• na + locative = being on/at something
• na + accusative = movement onto something

So:

• na polici = on the shelf (location)
• na policu = onto the shelf (movement)

In this sentence, the object is already located there, so na polici is correct.

Yes. They agree with the noun in gender, number, and case.

Here the noun is kaput, which is:

• masculine
• singular
• nominative

So you get:

• tvoj kaput
• moj (with kaput understood)

Compare:

• tvoja torba = feminine
• moje pismo = neuter
• tvoje knjige = plural

And in other cases:

• bez mog kaputa = without my coat
• sa tvojom torbom = with your bag

Not completely. Serbian word order is more flexible than English word order because case endings carry a lot of grammatical information.

The given sentence is a neutral, natural way to say it:

• Tvoj kaput je ispod stolice, a moj je iznad torbe na polici.

But you can change the order for emphasis:

• Ispod stolice je tvoj kaput.
  This emphasizes where the coat is.

One important limit: clitics like je still prefer second position in the clause.

It can be a little ambiguous, just like English above the bag on the shelf.

The most natural reading is usually:

• the bag is on the shelf
• my coat is above that bag

But if you want to make it absolutely clear, Serbian can be more explicit:

• a moj je iznad torbe koja je na polici
  = and mine is above the bag that is on the shelf

Or, if you mean that my coat is on the shelf, you could say:

• a moj je na polici, iznad torbe
  = and mine is on the shelf, above the bag

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

So forms like:

• stolice
• torbe
• polici

do not themselves tell you the vs a. That usually comes from context.

If speakers need to be more specific, they can use words like:

• taj = that
• ovaj = this
• jedan = a certain / one

But very often Serbian simply leaves this unspecified and lets context do the work.

They can be used with both, and they still normally take the genitive.

Examples:

• Kaput je ispod stolice. = The coat is under the chair.
• Stavi kaput ispod stolice. = Put the coat under the chair.

And:

• Lampa je iznad stola. = The lamp is above the table.
• Postavi lampu iznad stola. = Place the lamp above the table.

So unlike na, which changes case depending on location vs movement, ispod and iznad normally keep the genitive.