Park kapısı açılınca çocuklar içeri koşuyor.

Açılınca breaks down as:

• açıl- = to open / to be opened
• -ınca / -ince = when, once, as soon as

So açılınca means when it opens, once it opens, or as soon as it is opened, depending on context.

Because açmak means to open something, while açılmak means to open or to be opened.

• açınca = when someone opens it
• açılınca = when it opens / when it is opened

In this sentence, the subject is park kapısı (the park gate), so Turkish uses açıl-.

This is due to vowel harmony.

The last vowel in açıl- is ı, which is a back vowel, so the suffix appears as -ınca.

Compare:

• gelince = when he/she comes
• bakınca = when he/she looks
• açılınca = when it opens

Park kapısı is a very common Turkish noun compound pattern, similar to English park gate, school door, car door, etc.

Structure:

• park = park
• kapısı = its gate / gate of

Together, park kapısı means park gate.

You can also say parkın kapısı, but that sounds more like the gate of the park, with a more explicit possession relationship. In many everyday contexts, park kapısı is the more natural compact form.

That -sı is the 3rd person possessive suffix, which is also used in this kind of noun compound.

So:

• kapı = door / gate
• kapısı = its door / its gate

In compounds, Turkish often marks the second noun this way:

• okul bahçesi = school yard
• araba kapısı = car door
• park kapısı = park gate

Here it does not necessarily mean literal possession in the English sense; it is just part of the standard compound structure.

Yes. Kapı can mean both door and gate, depending on context.

So in:

• ev kapısı = house door
• bahçe kapısı = garden gate
• park kapısı = park gate

the English translation changes according to the situation.

İçeri means inside, in, or inward when there is movement toward the inside.

So içeri koşmak means to run inside.

It is very natural with motion verbs such as:

• girmek = to go in
• koşmak = to run
• yürümek = to walk

Because these forms mean different things:

• içeri = inside / inward movement
• içeride = inside location
• içine = into it / into its inside

Here the children are moving inward, so içeri is the right choice.

Compare:

• Çocuklar içeri koşuyor. = The children run inside.
• Çocuklar içeride oynuyor. = The children are playing inside.
• Top kutunun içine düştü. = The ball fell into the box.

In Turkish, when the subject is already clearly stated, the verb does not always need a plural ending.

So both of these are possible:

• Çocuklar içeri koşuyor.
• Çocuklar içeri koşuyorlar.

The version without -lar is very common and completely natural.

Yes, koşuyor is the present progressive form of koşmak.

But Turkish -yor is used a bit more broadly than English is/are ...-ing. It can describe:

• something happening right now
• a vivid scene
• a repeated situation, depending on context

So here it can sound like:

• a live scene: The gate opens and the children run inside
• or a usual pattern: When the gate opens, the children run inside

If you wanted a more plain habitual feel, koşar(lar) could also be possible in another context.

It can be either one, depending on context.

• As a scene: The park gate opens, and the children run inside.
• As a repeated pattern: Whenever the park gate opens, the children run inside.

The form -ınca often allows both when and whenever readings.

Turkish often puts the background or time information first, then gives the main action.

So this order is very natural:

• Park kapısı açılınca = when the park gate opens
• çocuklar içeri koşuyor = the children run inside

This helps set the scene before the main event.

Yes, Turkish word order is flexible, although some orders sound more natural than others.

For example, you could also say:

• Çocuklar park kapısı açılınca içeri koşuyor.

That is still understandable. But the original sentence sounds very natural because it gives the when-clause first, then the main action.

Because Turkish has no definite article like English the.

So words like:

• park kapısı
• çocuklar

do not directly show the or a/an. The listener understands that from context.

In English, this sentence will usually be translated with the because the gate and the children sound specific in context.