Pobednik je moj saigrač.

Je is the 3rd person singular present form of biti (to be) — so it means is.

In Serbian, short forms like je are clitics, and clitics usually go in second position in the sentence or clause. That is why you get:

Pobednik je moj saigrač.

Not usually:

Pobednik moj saigrač je.

So even though English puts is between subject and complement in a more fixed way, Serbian is also following a special clitic-placement rule here.

Both are in the nominative singular.

This sentence is an equational sentence: one noun is being identified as another noun.

• pobednik = nominative singular
• saigrač = nominative singular

So the structure is basically:

[Nominative noun] + je + [nominative noun phrase]

That is normal with biti when you are saying that one person or thing is another person or thing.

Because saigrač is a masculine singular noun, and the possessive adjective moj has to agree with it.

So:

• moj = masculine singular
• moja = feminine singular
• moje = neuter singular

Since saigrač is masculine, the correct form is:

moj saigrač

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

So pobednik can mean:

• a winner
• the winner

The exact meaning depends on context. In this sentence, English usually translates it as the winner because the sentence is identifying a specific person:

The winner is my teammate.

But Serbian does not need a separate word for the.

Yes. That is also correct.

Both sentences are grammatical:

• Pobednik je moj saigrač.
• Moj saigrač je pobednik.

The difference is mainly focus or emphasis.

• Pobednik je moj saigrač.
  Focuses more on the winner.

• Moj saigrač je pobednik.
  Focuses more on my teammate.

In English, both would often be translated similarly, but in Serbian word order can shift to highlight different information.

It is one word: saigrač.

It may look a little confusing because Serbian also has the preposition sa meaning with, but here saigrač is a single noun meaning teammate / fellow player.

Compare:

• igrač = player
• saigrač = teammate / fellow player

So you should not split it into sa igrač in this sentence.

• igrač means player
• saigrač means teammate or fellow player

The word saigrač refers specifically to someone on your side or on your team, not just any player.

So:

• On je igrač. = He is a player.
• On je moj saigrač. = He is my teammate.

A rough pronunciation guide is:

po-BED-neek ye moy SA-ee-grach

A few useful sound notes:

• j is pronounced like English y in yes
• č is like ch in chop
• Serbian spelling is quite phonetic, so words are usually pronounced as written

So:

• je sounds like ye
• moj sounds like moy
• saigrač has a clear č = ch sound at the end

Yes — in this exact sentence, saigrač is a masculine noun, so it normally refers to a male teammate.

If the teammate is female, you would usually use the feminine form:

saigračica = female teammate

So if both refer to a woman, you would say:

Pobednica je moja saigračica.

That changes:

• pobednik → pobednica
• moj → moja
• saigrač → saigračica

In standard Serbian, no — not in a normal sentence like this.

You need the verb:

Pobednik je moj saigrač.

Leaving out je would sound incomplete, unnatural, or highly nonstandard in this context.

So unlike some languages where is can be omitted in the present tense, Serbian normally keeps je here.

You change je to nije:

Pobednik nije moj saigrač.
= The winner is not my teammate.

That is the normal way to negate je.

You would change all the relevant words to plural:

Pobednici su moji saigrači.

Changes:

• pobednik → pobednici = winners
• je → su = are
• moj → moji
• saigrač → saigrači

So the sentence means:

The winners are my teammates.

Because possessive adjectives normally come before the noun they describe.

So:

• moj saigrač = my teammate
• moja knjiga = my book
• moj prijatelj = my friend

This works much like English, where my also comes before the noun.

So moj saigrač is the expected and natural order.