Arkadaşım yeni işine başlayınca onu biraz kıskandım, ama yine de çok sevindim.

Because -ım is the 1st person singular possessive suffix.

• arkadaş = friend
• arkadaşım = my friend

So Turkish often expresses my / your / his-her by adding a suffix to the noun instead of using a separate word.

Also, arkadaş is gender-neutral, so arkadaşım could mean my male friend or my female friend.

işine breaks down like this:

• iş = job, work
• -i = his/her (3rd person possessive)
• -ne = to (dative case, with a buffer n)

So işine means to his/her job or to their job.

This is used because the job belongs to the friend being talked about. Compare:

• yeni işe başlayınca = when he/she started a new job
• yeni işine başlayınca = when he/she started his/her new job

Also, the verb başlamak normally takes the dative case, so Turkish says something like start to a job.

başlayınca comes from başlamak = to start, to begin.

It is formed like this:

• başla- = start
• -yınca = when / once / after

So başlayınca means when he/she started or once he/she started.

The suffix has several forms depending on vowel harmony:

• -ınca
• -ince
• -unca
• -ünce

After a vowel, Turkish often inserts a buffer y, which is why it becomes başla-y-ınca.

Because kıskanmak takes a direct object in Turkish.

• o = he / she / it
• onu = him / her / it

So:

• onu kıskandım = I was jealous of him/her

This is different from English, where we say jealous of someone. Turkish does not use a separate word corresponding to of here; it uses the accusative object instead.

Both are in the simple past tense.

kıskandım

• kıskan- = be jealous / envy
• -dı = past tense
• -m = I

So: I was jealous / I envied

sevindim

• sevin- = be glad, become happy
• -di = past tense
• -m = I

So: I was glad / I became happy

The past tense endings change form by vowel harmony and consonant assimilation, so you may see -dı, -di, -du, -dü or -tı, -ti, -tu, -tü.

Because the verb ending already tells you the subject.

• kıskandım = I was jealous
• sevindim = I was glad

The -m ending marks first person singular, so Turkish often leaves out ben unless it is needed for emphasis or contrast.

You could say:

• Ben onu biraz kıskandım, ama yine de çok sevindim.

But the ben is not necessary.

biraz means a little, somewhat, or a bit.

So:

• onu biraz kıskandım = I was a little jealous of him/her

It softens the statement. Without biraz, the jealousy sounds stronger:

• onu kıskandım = I was jealous of him/her
• onu biraz kıskandım = I was a bit jealous of him/her

This is a very natural combination in Turkish.

• ama = but
• yine de = still / even so / nevertheless

So together, ama yine de means something like:

• but still
• but even so
• but nevertheless

Using both creates a stronger sense of contrast:

• I felt a bit jealous, but still I was very happy.

You can use only one of them in some contexts, but using both is common and natural.

Because Turkish often leaves things unsaid if the context already makes them clear.

Here, after hearing:

• Arkadaşım yeni işine başlayınca...

the listener already understands what the speaker is happy about: the friend's new job / the friend's success.

So çok sevindim by itself is enough. Turkish does this often when the missing information is obvious from the previous clause.

No. Turkish does not mark gender in this sentence.

• arkadaşım = my friend
• o / onu = he, she, it / him, her, it

So from the Turkish alone, you cannot tell whether the friend is male or female unless extra context is given.

This is very common in Turkish and can feel unusual for native English speakers at first.

It follows a very typical Turkish pattern.

A rough structure is:

• Arkadaşım yeni işine başlayınca = when my friend started his/her new job
• onu biraz kıskandım = I was a little jealous of him/her
• ama yine de çok sevindim = but I was still very happy

Turkish often puts the verb at the end of each clause:

• başlayınca
• kıskandım
• sevindim

That final-verb pattern is one of the most important things to get used to in Turkish.

Yes:

• Arkadaşım = my friend
• yeni = new
• işine = to his/her job
• başlayınca = when he/she started
• onu = him/her
• biraz = a little
• kıskandım = I was jealous / I envied
• ama = but
• yine de = still / nevertheless
• çok = very
• sevindim = I was glad / I became happy

This sentence is a good example of how Turkish packs a lot of meaning into suffixes rather than separate words.