Learn Hardcore Turkish: Çocuk salıncakta uyumuyor, sadece dinleniyor. - The child is not sleeping on the swing, he is just resting.

Because the last vowel of salıncak is back (a), the locative uses the back form: -da/-ta.
Because the final consonant k is voiceless, the suffix surfaces as -ta (not -da). So: salıncak + ta → salıncakta = “on/at the swing.”

Does salıncakta mean “on a swing” or “on the swing”?

Turkish doesn’t have articles like “a/the.” Bare çocuk and salıncakta are interpreted from context:

Specific/known: “on the swing,” “the child”
Non-specific: usually marked with bir: Bir çocuk salıncakta… = “A child is on a swing…” In your sentence, it most naturally reads as “the child … on the swing.”

Why is it uyumuyor and not something like uyumayor or uyumıyor?

Negated present continuous is formed as: verb stem + negative + -(I)yor, but in practice the negative and -(I)yor fuse into -mIyor. The vowel I harmonizes with the last vowel of the stem.

Stem: uyu- (from uyumak, “to sleep”; last vowel: u)
Negative + prog.: -mIyor → -muyor (because of the u) Result: uyu + muyor → uyumuyor = “is not sleeping.”
Compare: gelmiyor (not coming), okumuyor (not reading), yazmıyor (not writing).

Why can’t I negate with değil (e.g., “uyuyor değil”)?

Değil negates nominal/adjectival predicates, not verbs. Verbs take the built-in negative suffix -ma/-me (here fused as -mIyor in the present continuous).
However, you can use değil with a noun phrase: Uykuda değil = “(He/She) is not asleep.”

What does sadece mean, and how does it compare to yalnız or yalnızca?

sadece = “only, just” (unambiguous, very common).
yalnızca = near-synonym of sadece (slightly more formal).
yalnız can mean “only,” but also “alone,” so it can be ambiguous out of context.
In your sentence, sadece clearly means “only/just.”

Where should sadece go, and does position change the meaning?

Yes; sadece directly before what it limits:

Çocuk salıncakta uyumuyor, sadece dinleniyor. = He isn’t sleeping; he’s only resting. (only = the action)
Çocuk sadece salıncakta dinleniyor. = He rests only on the swing (not elsewhere). (only = the location)
Sadece çocuk salıncakta dinleniyor. = Only the child is resting on the swing (others aren’t). (only = the subject)

Why is the subject omitted in the second clause (sadece dinleniyor)?

Turkish is pro-drop: once the subject is clear, it’s usually dropped. The subject (çocuk) carries over from the first clause, so (o) sadece dinleniyor → sadece dinleniyor is natural.

Do I need a conjunction like ama (“but”) between the clauses?

Not required. A comma is enough for a contrast. You could add ama or fakat:

Çocuk salıncakta uyumuyor, ama sadece dinleniyor.
Or a semicolon: Uyumuyor; sadece dinleniyor.

What nuance does -yor have here? How is uyumuyor different from uyumaz?

-yor is the present continuous (right now, ongoing, or currently true).

uyumuyor = “is not sleeping (now/at the moment/these days).”
The aorist -r/-maz expresses habits/general truths:
uyumaz = “(He/She) doesn’t sleep (habitually).”

Could I write salıncakda with -da?

No. With a voiceless final consonant like k, the locative uses -ta/-te, not -da/-de. Hence salıncakta.
More examples: parkta, bankta, but evde, okulda (voiced consonant → -da/-de).

How do I say “to the swing” and “from the swing”?

Dative (to/toward): salıncağa (salıncak + (y)a; ğ shows vowel-lengthening in writing)
Ablative (from): salıncaktan (salıncak + tan)

How are c and ç pronounced in Çocuk salıncakta?

ç = “ch” as in “chocolate” → Çocuk starts with “cho-”.
c = “j” as in “jam” → salıncak has a “j” sound in the middle.
So: “CHO-juk sa-lın-JAK-ta.”

Can I move salıncakta elsewhere in the sentence?

Yes, word order is flexible for emphasis:

Çocuk salıncakta uyumuyor, sadece dinleniyor. (neutral)
Çocuk uyumuyor, sadece salıncakta dinleniyor. (emphasizes location for the resting)
Salıncakta çocuk uyumuyor, sadece dinleniyor. (fronts the location; more marked style)

Is there a more formal or alternative way to say “is resting”?

Yes:

dinlenmekte (very formal/literary continuous): Çocuk … dinlenmekte.
istirahat ediyor (formal/medical): Çocuk … istirahat ediyor.
Everyday speech prefers dinleniyor.

Do I need an apostrophe before the case suffix (salıncak’ta)?

No. Apostrophes are only used with proper names: Ankara’da, Ahmet’i.
Common nouns like salıncak take suffixes without an apostrophe: salıncakta.