Learn Hardcore Turkish: Kafamda aynı şeyler bir döngü hâlinde dönüp duruyor. - The same things keep going around in a loop in my head.

Kafamda = kafa (head) + possessive -m (my) → kafam
- locative -da (in/at/on) → kafamda = in my head.
The -da here is the locative case suffix, not the clitic de/da meaning also/too.
Choice of -da/-de/-ta/-te follows consonant voicing and vowel harmony. Because kafam ends with a voiced consonant (m), you use -da (not -ta).

Why is the verb singular (dönüp duruyor) even though the subject (aynı şeyler) is plural?

In Turkish, third-person plural agreement on the verb is optional. With non-human or indefinite plural subjects, the verb usually stays singular. So aynı şeyler … dönüp duruyor is the natural choice. You’d generally use -lar/-ler on the verb mainly for human, specific subjects or when you want to emphasize the plurality: Çocuklar geldi(ler). Here, dönüp duruyorlar would sound odd or unnecessarily heavy.

What nuance does dönüp duruyor add compared to just dönüyor?

dönüyor = is turning/going around (plain ongoing action).
dönüp duruyor = keeps turning around, over and over, often with a sense of persistence, monotony, or mild annoyance. Literally it looks like turning and standing, but durmak acts as an aspectual auxiliary here and does not mean to stop.
Close English feel: keep V‑ing / V‑ing on and on.

What is the function of the -ıp/-ip/-up/-üp ending in dönüp?

It’s the converb (adverbial participle) that links verbs, often translated as and V‑ing or after V‑ing. It follows vowel harmony: dön- has ö (front rounded), so you get -üp → dönüp. In the pattern V‑ip durmak, it signals repeated/continuous action:

söyleyip duruyor = he keeps saying (it).
arayıp duruyor = she keeps calling.
yazıp duruyor = they keep writing.

What does bir döngü hâlinde mean structurally, and why the circumflex in hâlinde?

X hâlinde literally means in the state/form of X. It’s built from hâl (state) + 3rd person possessive -i
- locative with buffer -n- → hâl‑i‑nde.
So bir döngü hâlinde ≈ in the form of a loop / in a loop-like state.
The circumflex â marks a long vowel (from Arabic-origin hâl). Modern texts often write halinde without the circumflex; both are accepted.

Can I omit bir and just say döngü hâlinde?

Yes. bir döngü hâlinde and döngü hâlinde are both fine. With bir, it feels a touch more like in a (kind of) loop; without bir, it’s a bit more generic/abstract. The difference is subtle here.

Is the word order fixed? Can I move the parts around?

Turkish word order is flexible, and you can front what you want to topicalize or emphasize. All of these are acceptable:

Aynı şeyler kafamda bir döngü hâlinde dönüp duruyor.
Kafamda aynı şeyler bir döngü hâlinde dönüp duruyor.
Kafamda bir döngü hâlinde aynı şeyler dönüp duruyor. Default is to place setting (locative) and subject before the verb cluster.

Could I just say Kafamda aynı şeyler dönüyor? What changes?

You can. It’s simpler and perfectly natural, but it loses the built-in sense of ongoing repetition/irritation that dönüp duruyor gives. If you drop dönüp duruyor and/or bir döngü hâlinde, you can add an adverb to keep the same feel:

Kafamda aynı şeyler hep/sürekli dönüyor.

Is dönüp dönüyor acceptable?

Not really in this meaning. The idiomatic pattern for repeated action is V‑ip durmak (here: dönüp duruyor). You may see dönüp dönüp used adverbially before another verb (e.g., dönüp dönüp bakmak = to keep glancing back), but dönüp dönüyor sounds awkward.

Why not say benim kafamda? Do I need the pronoun?

No. The possessive suffix -m in kafam already says my. Benim kafamda is used only for contrast/emphasis (e.g., Not in your head—in mine: Benim kafamda …).

What’s the difference between kafamda, aklımda, zihnimde, and başımda?

kafamda: literally in my head; common, neutral in everyday talk about thoughts.
aklımda: on my mind/in my mind; focuses on memory/consideration (plans, reminders).
zihnimde: in my mind/intellect; a bit more formal or literary.
başımda: on/over my head; often physical or figurative burdens (e.g., başımda dert var = I’m in trouble).

Why şeyler (plural)? Could I say aynı şey (singular)?

Both are possible:

aynı şey: the same one thing/concept keeps recurring.
aynı şeyler: several recurring items/topics. In everyday speech about thoughts, the plural feels quite natural.

Could I use plural agreement on the verb: dönüp duruyorlar?

Grammatically possible but stylistically off here. With non-human or indefinite plurals like aynı şeyler, Turkish strongly prefers a singular verb. Use plural agreement chiefly for human, specific subjects when you want to stress plurality.

How do vowel harmony rules explain -da and -üp here?

-da/-de/-ta/-te (locative): choose d/t by the voicing of the preceding consonant and a/e by the last vowel. kafam ends with voiced m and has back vowel a, so -da → kafamda.
-(y)ıp/-(y)ip/-(y)up/-(y)üp (converb): match the last vowel of the stem. dön- has ö (front rounded), so -üp → dönüp.

Any pronunciation tips for dönüp, hâlinde, şeyler?

ö and ü are front rounded vowels (like French eu and u). Keep lips rounded.
şeyler is roughly shey-ler; ey like the vowel in day.
hâlinde/halinde both pronounced with a longish a for many speakers; the circumflex simply reminds you of that length.

Is there a register or tone difference in this wording?

Overall it’s natural and conversational. The phrase bir döngü hâlinde leans a bit literal/bookish; you could make it more casual with adverbs:

Kafamda aynı şeyler sürekli/hep dönüp duruyor.

Are there close synonyms for bir döngü hâlinde?

Yes, depending on tone:

bir döngü gibi (like a loop) — more colloquial.
döngü şeklinde (in the form of a loop).
You also hear the set phrase kısır döngü (vicious circle), e.g., kafamda kısır bir döngü var, which adds a negative, stuck-in-a-rut nuance.