Learn Hardcore Turkish: Buluşma bitmek üzereyken yeni bir soru geldi. - When the meetup was about to end, a new question came.

Here it means “about to, on the verge of.” So bitmek üzere = “about to end.”
The same üzere can also mean “with the purpose of” with motion/intent verbs: e.g., Sizi görmek üzere geldim = “I came to see you.” In bitmek üzereyken, it’s clearly the “about to” meaning.

What does -yken add, and why is there a y?

-ken means “when/while.” It turns what comes before it into a time clause.
After a vowel, Turkish inserts a buffer y: üzere + y + ken → üzereyken.
Compare: evdeyken (“while at home”), gelirken (“while coming”), mutluyken (“when (someone is) happy”).

How is bitmek üzereyken built morphologically?

bit- (finish) + -mek (verbal noun) + üzere (about to) + -yken (when/while) → “when [it] was about to finish.”
The understood subject of that clause is buluşma (“the meeting”).
No personal ending is needed because this is an adverbial time clause; the finite past is in geldi.

Could I say Buluşma bitiyorken or Buluşma biterken instead? What’s the nuance?

bitiyorken ≈ “while it was ending” (process in progress).
biterken ≈ “as it was ending/coming to an end.”
bitmek üzereyken emphasizes imminence: “just about to end.” It feels tighter/more immediate than the others.

Why isn’t there a past marker like -di in the first clause?

-yken already subordinates the clause as a time phrase. The main tense is carried by geldi.
As a standalone main clause you’d say: Buluşma bitmek üzereydi (“The meeting was about to end.”)

What’s the role of bir in yeni bir soru? Can I omit it?

bir works like the English “a/an” here.
You can omit it (yeni soru geldi), but with bir it sounds more natural and specific in everyday speech: “a single new question (popped up).”

Is yeni bir soru the subject? Why is it before geldi?

Yes, yeni bir soru is the subject of geldi (“came”).
Turkish typically places the finite verb at the end; time/adverbial clauses often come first, then the subject, then the verb.

Why use gelmek with a question? Would soruldu be better?

soru geldi is idiomatic: “a question came (in/up),” like messages or calls “come.”
soru soruldu (“a question was asked”) is also correct; it highlights the (unspecified) asker more than the arrival.
Both are fine; geldi feels a bit more conversational.

Do I need a comma after the first clause?

Preferred: Buluşma bitmek üzereyken, yeni bir soru geldi.
You’ll see it omitted informally, but standard punctuation uses the comma after a fronted adverbial clause.

Could I use gelmiş instead of geldi? What changes?

geldi: direct past (the speaker presents it as a known/observed fact).
gelmiş: inferential/reported past (the speaker learned it indirectly or later).
Here, geldi is the neutral, expected choice.

Is there a more formal alternative using sıra/sırada or olmak?

Yes: Buluşmanın bitmek üzere olduğu sırada yeni bir soru geldi.
This uses a relative clause (…olduğu) plus sırada (“at the time when”). It’s longer/more formal but equivalent in meaning.

What’s the difference between buluşma, görüşme, and toplantı?

buluşma: a meetup/rendezvous; can be casual or even a date.
görüşme: a meeting/discussion/interview between parties.
toplantı: a formal meeting (work/official). In business contexts, toplantı is most common.

Can I say Tam … -yken to mean “just as …”?

Yes. Tam buluşma bitmek üzereyken yeni bir soru geldi. = “Just as the meeting was about to end, a new question came.”

How would I express an interrupted plan like “when it was going to end (but then…)”?

Use future + -ken: Buluşma bitecekken yeni bir soru geldi. This often implies the expected ending was interrupted or delayed by what followed.