Learn Hardcore Turkish: Arkadaşım gelince seviniyorum.

It forms a time clause meaning when/whenever. So gelince = when (someone) comes. It doesn’t itself mark tense; the main clause verb (seviniyorum) sets the time frame.

Why is it gelince and not geldiğinde?

Both are correct:

Arkadaşım gelince seviniyorum is shorter and very common.
Arkadaşım geldiğinde seviniyorum uses the -dik + possessive + -de structure, which can mark the subject on the verb (e.g., geldiğimde = when I come). It can sound a bit more explicit/formal. Meaning is essentially the same here.

How does vowel harmony decide the form of -ince? What are the other shapes?

The suffix has 4-way harmony and a buffer -y- after vowels:

After front unrounded (e, i): -ince → gelince
After front rounded (ö, ü): -ünce → gülünce
After back unrounded (a, ı): -ınca → kalayınca
After back rounded (o, u): -unca → konuşunca
If the verb stem ends in a vowel, use -y-: başla → başlayınca

How is -ince different from -ken?

-ince = when/whenever (event boundary): Gelince aradı = He called when he arrived.
-ken = while/during (overlap in time): Gelirken aradı = He called while he was on the way.

Why is seviniyorum in the -yor form if this is a general/habitual statement? Can I say sevinirim?

Turkish often uses -yor for typical reactions and current habits: Seviniyorum = I get happy (whenever that happens).
You can also say Sevinirim (aorist), which is more general or slightly hypothetical/polite. Both can work; -yor sounds very natural for recurring feelings.

Can you break the sentence down?

Arkadaş-ım = friend + my (1sg possessive) → my friend
gel-ince = come + when/whenever
sevin-iyor-um = be glad/rejoice + progressive + 1sg → I am (get) happy

Do I need to say ben?

No. The ending -um in seviniyorum already shows the subject is I. You can add Ben for emphasis: Ben arkadaşım gelince seviniyorum.

Why isn’t it Arkadaşımı with the accusative?

Because arkadaşım is the subject of the time clause (arkadaşım gelince = when my friend comes). Subjects are unmarked (no case). Accusative marks a definite direct object. Compare: Arkadaşımı görünce seviniyorum = I get happy when I see my friend (here, friend is the object of görmek).

Does gelince mean a specific time or “whenever”?

It can be either, depending on the main verb’s tense/aspect:

Habitual/whenever (present): … seviniyorum.
Specific past: Arkadaşım gelince sevindim = I was happy when my friend came.
Future: Arkadaşım gelince sevineceğim = I will be happy when my friend comes.

Can -ince show who is doing the action, like “when I come”?

Not by suffix alone. Use:

A pronoun/noun: Ben gelince…, Ali gelince…
Or the -dik + possessive + -de form: Geldiğimde (when I come), geldiğinde (when you/he/she comes), geldiğimizde (when we come), etc.

How do I say “as soon as my friend comes”?

Use -er/-mez: Arkadaşım gelir gelmez seviniyorum (or future: sevineceğim). This is stronger/immediate compared to gelince.

What’s the nuance of sevinmek vs mutlu olmak vs sevindirmek?

sevinmek: to feel glad/pleased (often for a specific trigger). Natural here.
mutlu olmak: to become/be happy (broader, a bit more formal/neutral): Arkadaşım gelince mutlu oluyorum.
sevindirmek: to make someone happy (causative): Arkadaşımın gelmesi beni sevindiriyor = My friend’s coming makes me happy.

Can I change the word order?

Yes, for emphasis:

Neutral: Arkadaşım gelince seviniyorum.
Focus on the feeling: Seviniyorum, arkadaşım gelince.
Emphasize the subject: Ben, arkadaşım gelince seviniyorum.
Turkish prefers the time clause before the main clause, but postposing it is possible for focus/style.