Ben kardeşimi kıskanmıyorum; onun başarısıyla gurur duyuyorum.

Because it adds emphasis or contrast.

Turkish often leaves out subject pronouns when the verb ending already shows the person. So:

• kıskanmıyorum already means I am not jealous / I’m not envying
• duyuyorum already means I feel / I am feeling

That means the sentence could also be:

• Kardeşimi kıskanmıyorum; onun başarısıyla gurur duyuyorum.

Using Ben makes the speaker more explicit, often with a feeling like as for me or I personally.

It is:

• kardeş = sibling / brother / sister
• -im = my
• -i = accusative case

So kardeşimi means my sibling as the direct object of the verb.

A useful thing to remember: kardeş is gender-neutral. It can mean brother or sister, depending on context.

Because kıskanmak takes a direct object, and here that object is specific: my sibling.

In Turkish, specific definite direct objects usually take the accusative. So:

• kardeşim = my sibling
• kardeşimi = my sibling, as the object

Here, the person being envied or felt jealous of is the object, so kardeşimi is the correct form.

It breaks down like this:

• kıskan- = be jealous of / envy
• -ma / -me = negative
• -iyor = present continuous
• -um = I

So the structure is basically:

• kıskan-ma-ıyor-um

But in actual Turkish, this contracts to:

• kıskanmıyorum

So it means I am not jealous or I’m not envying.

Yes, but Turkish uses the present continuous for ongoing states and attitudes very naturally.

So kıskanmıyorum does not have to mean only at this exact second I am not being jealous. It can also mean:

• I’m not jealous
• I’m not feeling jealousy toward my sibling
• That isn’t how I feel

Likewise, gurur duyuyorum can mean I’m proud in a natural, general-present way.

It can cover both ideas, depending on context.

In English, jealousy and envy are often separated more carefully. Turkish kıskanmak is broader and can be used for feelings that English might translate as:

• to be jealous of
• to envy
• sometimes to be possessive about

In this sentence, the intended meaning is clearly the non-positive feeling toward the sibling’s success, which English may express as either I’m not jealous of my sibling or I don’t envy my sibling.

Naturally, it means:

• I am proud
• I feel proud

Literally, duymak often means to hear, but it can also mean to feel / sense / experience in some expressions.

So gurur duymak is a set expression meaning to feel pride or to be proud.

It is best learned as a chunk:

• gurur duymak = to be proud

Because gurur duymak is the usual way to say to be proud of someone/something.

• gurur duyuyorum = I am proud
• gururluyum = I am proud / proud-natured / prideful

The adjective gururlu can sometimes sound more like a personality trait or a proud bearing, and in some contexts it can even feel closer to prideful. But gurur duymak is the standard expression when you mean:

• I’m proud of my sibling
• I’m proud of that success

So in this sentence, gurur duyuyorum is the most natural choice.

It breaks down like this:

• onun = his / her / its
• başarısı = his/her success
• -yla = with / by means of / because of, from ile

So:

• onun başarısıyla = with his/her success in form

But in this sentence, the natural English meaning is:

• of his/her success
• because of his/her success
• regarding his/her success

With gurur duymak, Turkish commonly uses this -la / -le / -yla / -yle pattern.

Because the success belongs to him/her — in context, to the sibling.

• başarı = success
• başarısı = his/her success

That -sı is the third-person possessive ending.

So:

• onun başarısı = his/her success

Then when -yla is added, it becomes:

• onun başarısıyla

Because -yla / -yle is a common attached form of ile.

So these are equivalent in meaning:

• başarısıyla
• başarısı ile

The attached version is usually smoother and more common in everyday Turkish.

The y appears because the word already ends in a vowel sound, so Turkish uses a buffer consonant:

• başarısı + ile → başarısıyla

Yes, often it could.

Turkish often leaves out possessive pronouns when the possessive ending already makes the meaning clear. So:

• başarısıyla gurur duyuyorum

can already mean:

• I’m proud of his/her success

if the context clearly shows whose success it is.

However, onun is useful here because it makes the reference explicit and creates a nice contrast with the first clause.

Yes, definitely.

That would mean:

• with my sibling’s success
• naturally, of my sibling’s success

So this version is also correct:

• Ben kardeşimi kıskanmıyorum; kardeşimin başarısıyla gurur duyuyorum.

The sentence you were given uses onun to avoid repeating kardeş and to sound a bit smoother.

No. Both are gender-neutral.

• kardeş = sibling / brother / sister
• onun = his / her / its

Turkish does not have separate everyday third-person singular pronouns for he and she. So the sentence does not tell you whether the sibling is a brother or a sister unless extra words are added.

Not completely, but the given order is very natural.

Turkish usually puts the verb at the end, so both clauses follow a common pattern:

• Ben kardeşimi kıskanmıyorum
• onun başarısıyla gurur duyuyorum

This order sounds neutral and clear. Other orders are possible for emphasis, but the version you have is a very good standard model.

It joins two closely related clauses:

• I’m not jealous of my sibling
• I’m proud of his/her success

So the second clause explains or reinforces the first one. It shows a contrast between a negative feeling that is denied and a positive feeling that is affirmed.

You could also write this as two separate sentences, but the semicolon neatly links the ideas.