Learn Hardcore Turkish: Uygulama kaydırınca takılıyor; siz çıktı alın, ben onay kutusunu işaretleyeyim. - The app lags when you scroll; you print, and I’ll tick the checkbox.

It’s the temporal adverbial suffix -(I)nca/-(I)nce/-(U)nca/-(Ü)nce, meaning “when/once/whenever.”
Breakdown: kaydır- (to swipe/make slide) + -ınca → kaydırınca = “when (you) swipe.”

Who is actually doing the swiping in Uygulama kaydırınca takılıyor? The app?

Not the app. In -ınca/-ince clauses the subject can be left implicit and understood from context. Here it means “when you/one swipes (the screen/list), the app freezes.” If you want to make the subject explicit and polite, you can say:

Kaydırdığınızda uygulama takılıyor (“when you [polite/plural] swipe, the app freezes”). If you want the passive (“when it is swiped”), use:
Kaydırılınca uygulama takılıyor.

Why kaydırmak and not kaymak?

kaymak = to slip/slide by itself.
kaydırmak = to make something slide; in phone/UX contexts it corresponds to “to swipe/scroll (something).”
So for swiping content with your finger, kaydırmak is the normal choice.

Could I say kaydırdığınızda instead of kaydırınca? Any difference?

Yes. Kaydırınca is colloquial/neutral and leaves the subject generic. Kaydırdığınızda is more explicit and polite/formal (it contains “your [pl.]” in the suffix), clearly anchoring the subject as “you (plural/formal).” Meaning-wise, both are “when you swipe.”

Why use takılıyor (present continuous) instead of takılır (aorist)?

Both can work:

takılıyor suggests an ongoing/repeated issue you’re experiencing (“it keeps freezing/it freezes when that happens”).
takılır feels more like a general rule/habitual statement.
In everyday tech complaints, takılıyor is very common.

Is donuyor a good alternative to takılıyor here?

Yes, with a nuance difference:

takılmak: to lag/stutter/get stuck (can be temporary).
donmak: to freeze (often a harder freeze).
Choose based on severity: takılıyor (laggy), donuyor (hard freeze).

Is the word order Uygulama kaydırınca takılıyor normal, or should kaydırınca come first?

It’s fine as is. Adverbial clauses like kaydırınca are mobile. You can also say:

Kaydırınca uygulama takılıyor (very common)
Uygulama, kaydırınca, takılıyor (less common; commas mark it off).
Fronting kaydırınca slightly emphasizes the condition.

Why is there a semicolon here?

The semicolon links two closely related independent parts: the problem and the proposed plan. A period would also be fine. A comma would be too weak (it risks a comma splice), while a dash could add an informal “so/therefore” feel.

Why use siz and the plural imperative alın? Could it be sen al?

siz … alın: polite/formal or addressing more than one person.
sen … al: informal/singular.
Both are grammatically correct; the choice reflects politeness and who you’re addressing.

What does çıktı almak mean? Is it literal “take output”?

It’s an idiomatic everyday phrase meaning “to print (a printout).”
Alternatives:

yazdırmak: to send to the printer/print (more technical/specific).
yazıcıdan çıktı almak: “to get a printout from the printer.”

Why isn’t there an accusative on çıktı (not çıktıyı)?

Because it’s indefinite and used as part of the fixed expression çıktı almak. If you mean a specific printout, you can add accusative:

Şu çıktıyı alın = “Take that printout.”

Why does onay kutusunu have both -su- and -nu?

It’s a noun compound plus accusative:

onay kutusu = “checkbox” (literally “approval box”), where -su is the 3rd person possessive used in noun-noun compounds.
As a specific direct object, it takes the accusative -(y)ı/-(y)i/-(y)u/-(y)ü. Since kutusu ends in a vowel, we add a buffer -n-: kutusu + nu → kutusunu.

What form is işaretleyeyim? Why that spelling?

It’s the 1st person singular optative/voluntative: “let me tick/mark.”
Breakdown: işaretle- (to mark/tick) + -yeyim (1sg optative). The glide -y- prevents a vowel clash: işaretle + y + eyim → işaretleyeyim.
Negative: işaretlemeyeyim (“let me not tick it”).
Suggestion form: İşaretleyeyim mi? (“Shall I tick it?”).

Are the pronouns siz and ben necessary here?

Not strictly. Turkish usually drops subject pronouns. They’re included here for contrast/division of labor: Siz do X, ben will do Y. You could add de for a smoother “and I’ll…”:

Siz çıktı alın, ben de onay kutusunu işaretleyeyim.

Could I say onay kutusunu seçeyim or tıklayayım instead of işaretleyeyim?

Yes, depending on UI action:

işaretlemek: tick/check (checkboxes).
seçmek: select (general).
tıklamak: click.
For a checkbox, işaretlemek is the most precise.

Is Uygulama kaydırınca takılıyor missing an object like “screen”?

In practice, Turkish often omits the obvious object in this context. If you want to be explicit:

Ekranı kaydırınca uygulama takılıyor (“When you swipe the screen…”),
or Uygulamada kaydırınca uygulama takılıyor (“When swiping in the app…”).
The original is natural and relies on context.

Any register alternatives for the imperative part?

Very polite request: Çıktı alır mısınız? (“Would you print?”)
Formal imperative: Çıktı alınız (polite but can sound stiff/official).
The optative for yourself stays natural: Ben onay kutusunu işaretleyeyim.