Learn Hardcore Turkish: Projeyi tamamlamak üzere herkes salonda yerini aldı. - Everyone took their place in the hall in order to complete the project.

Here -mek üzere expresses purpose: “in order to / for the purpose of (doing).” It’s a bit more formal and procedural than için. You can often substitute için with little change in meaning: Projeyi tamamlamak için… sounds slightly more neutral/colloquial; …-mek üzere feels more official/planned.

Can -mek üzere also mean “about to”?

Yes, but that sense typically appears with olmak: Projeyi tamamlamak üzereyiz = “We are about to complete the project.” In your sentence, without olmak, it’s the purpose reading (“to complete”).

Why is Projeyi in the accusative (-i)?

Because the project is specific/definite (“the project”), even inside this purpose clause. In Turkish, definite direct objects take accusative. If you meant “a project” (non-specific), you’d say proje tamamlamak üzere (no accusative).

Who is understood to be doing the tamamlamak (“completing”)?

By default, the subject of the -mek üzere clause is the same as the main clause subject. Here it’s herkes (“everyone”). So: “Everyone … took their seat (so that they could) complete the project.”

What exactly does yerini aldı mean?

Literally “took his/her place,” idiomatically “took their seat/position.” Morphology: yer (place) + -i (3rd person singular possessive → yeri, “his/her place”) + -(n)i (accusative → yerini) + aldı (took).

Why is the verb aldı singular after herkes?

Herkes is grammatically singular in Turkish, so it takes a singular verb: Herkes … aldı. Semantically it’s plural, but agreement is singular.

Can I say yerlerini aldı or use plural verb aldılar with herkes?

Herkes yerini aldı is the standard form.
Herkes yerlerini aldı is common in speech to reflect the plural meaning; many speakers find it natural.
Herkes … aldılar (plural verb) occurs in colloquial speech but is less standard; formal writing prefers singular agreement.

What’s going on with salonda? Why -da and not -de/ta/te?

It’s the locative suffix -DA:

Vowel harmony: previous vowel is back (o) → use -da (not -de).
Consonant assimilation: the word ends with a voiced consonant (n), so use d (not t). Hence salon + da → salonda. Compare: parkta (ends with voiceless k → t).

Can I move the purpose clause around? Is a comma needed?

Yes, word order is flexible:

Projeyi tamamlamak üzere herkes salonda yerini aldı. (given)
Herkes, projeyi tamamlamak üzere, salonda yerini aldı.
Salonda herkes, projeyi tamamlamak üzere, yerini aldı. A comma after an initial adverbial phrase is common but optional; use it for clarity/emphasis.

Why not proje tamamlamak üzere without accusative?

You can, but it then means “to complete a project (unspecified).” Using projeyi marks it as a specific, known project.

What’s the nuance difference between tamamlamak and bitirmek?

Both mean “to finish/complete.” Tamamlamak is a bit more formal/technical (“to bring to completion”), while bitirmek is the everyday “to finish.” Either would fit here: Projeyi bitirmek üzere… is fine.

Could I say Herkes salonda oturdu instead of yerini aldı?

You could, but it changes nuance. Oturdu = “sat (down).” Yerini aldı emphasizes taking one’s assigned/appropriate place or position (more event-like and idiomatic in organized settings).

What does salon mean here—“living room” or “hall”?

Salon can mean either. In a home context it’s “living room,” but in institutional/organizational contexts it’s “hall/auditorium.” The context here suggests a hall or meeting room.

Can the subject of the -mek üzere clause be different from the main subject?

Not with -mek üzere alone; its subject is controlled by the main clause subject. To specify a different subject, use a finite-like nominalization: Projeyi tamamlamaları için onları salona çağırdım (“I called them to the hall so that they would complete the project”).

Is there a difference between yerini almak and yer almak?

Yes:

Yerini almak = “to take one’s seat/position.”
Yer almak = “to take place / to be located / to appear (in a list, news, etc.).” They’re not interchangeable in this sentence.