Kapı açık olunca sokaktaki gürültüyü duyabiliyorum.

Both are possible, but they are not exactly the same in feel.

• açık olunca = when/once/since it is open
• açıkken = while it is open

In this sentence, olunca links the condition or situation to the result:
Kapı açık olunca ... duyabiliyorum = When the door is open, I can hear ...

It is built from olmak (to be / to become) + -ınca.

So:

• Kapı açıkken sokaktaki gürültüyü duyabiliyorum.
  = I can hear the street noise while the door is open.
• Kapı açık olunca sokaktaki gürültüyü duyabiliyorum.
  = When the door is open / if the door is open, I can hear the street noise.

In many contexts, they are very close.

-ınca / -ince / -unca / -ünce is a suffix meaning something like:

• when
• once
• sometimes if or whenever, depending on context

It attaches to a verb stem.

Examples:

• gelince = when he/she comes
• bitince = when it finishes
• açılınca = when it opens
• olunca = when it is / when it becomes

In your sentence:

• olunca = when it is / when it becomes
• açık olunca = when it is open

The vowel changes by vowel harmony:

• -ınca
• -ince
• -unca
• -ünce

Because açık is an adjective meaning open, and Turkish often uses olmak with adjectives to express a situation like being X or becoming X, especially before suffixes like -ınca.

You cannot normally attach -ınca directly to the adjective açık. You need a verb, so Turkish uses olmak:

• açık = open
• açık olmak = to be open
• açık olunca = when it is open

So this is a very normal structure:

• hazır olunca = when it is ready
• müsait olunca = when he/she is available
• sessiz olunca = when it is quiet

In Turkish, present-tense to be is often omitted in simple statements.

So:

• Kapı açık. = The door is open.
• literally, Turkish just says door open

This is completely normal. Turkish does not need an independent word like English is in these basic present-tense adjective sentences.

But when you need extra grammar attached, Turkish often uses olmak:

• Kapı açık. = The door is open.
• Kapı açık olunca... = When the door is open...

Because sokaktaki means the one that is in/on the street.

Breakdown:

• sokak = street
• sokakta = in/on the street
• sokaktaki = the one that is in/on the street

Here it modifies gürültü:

• sokaktaki gürültü = the noise in the street / the street noise

The suffix -ki turns a location phrase into something adjective-like.

Compare:

• masadaki kitap = the book on the table
• odadaki insanlar = the people in the room
• sokaktaki gürültü = the noise in the street

So sokakta gürültü would not fit the same way here.

-ki is a very common suffix that means something like the one in/on/at... or turns a phrase into a modifier.

Here is the structure:

• sokak = street
• sokakta = in/on the street
• sokaktaki = the one that is in/on the street

Then:

• sokaktaki gürültü = the noise that is in the street
  more naturally: the noise in the street

It is often used after location endings:

• evdeki çocuk = the child in the house
• çantadaki telefon = the phone in the bag
• dünkü toplantı = yesterday’s meeting (a related use)

So -ki is often very useful for making descriptive phrases.

Because gürültü is the direct object of duymak (to hear), and it is specific/definite here, so it takes the accusative ending.

• gürültü = noise
• gürültüyü = the noise as a specific object

This is the Turkish accusative suffix.

Why the extra y?

Because the noun ends in a vowel, so Turkish adds a buffer consonant:

• gürültü + ü would be awkward
• so it becomes gürültü + y + ü = gürültüyü

Compare:

• kitabı okuyorum = I am reading the book
• suyu içiyorum = I am drinking the water
• gürültüyü duyuyorum = I hear the noise

It comes from vowel harmony.

The accusative suffix is one of these:

• -ı
• -i
• -u
• -ü

If the noun ends in a vowel, a buffer y is added:

• -yı
• -yi
• -yu
• -yü

The last vowel in gürültü is ü, so the correct form is:

• gürültü + yü = gürültüyü

This is standard Turkish vowel harmony.

It means I can hear or I am able to hear.

Break it down:

• duy- = hear
• -abil- = can / be able to
• -iyor- = present continuous
• -um = I

So:

• duyabiliyorum = I can hear

This is the ability/possibility form of the verb.

Compare:

• duyuyorum = I hear / I am hearing
• duyabiliyorum = I can hear / I’m able to hear

In this sentence, the meaning is not just that hearing happens, but that the open door makes it possible.

Because the sentence emphasizes ability/possibility.

• duyuyorum = I hear it
• duyabiliyorum = I can hear it

The idea is:

When the door is open, I am able to hear the noise in the street.

That sounds natural because the open door creates the condition that allows the hearing.

If you said:

• Kapı açık olunca sokaktaki gürültüyü duyuyorum

that would also be understandable, but it feels more like I hear it as a fact.
duyabiliyorum stresses that the sound becomes audible / possible to hear.

Yes, sometimes -ınca/-ince can feel like when, once, since, or even because, depending on context.

In this sentence:

• Kapı açık olunca sokaktaki gürültüyü duyabiliyorum

possible natural translations include:

• When the door is open, I can hear the noise in the street.
• If the door is open, I can hear the noise in the street.
• Since the door is open, I can hear the noise in the street.
  (less likely as a default translation, but possible in the right context)

Usually when/if is the safest understanding here.

Yes, Turkish word order is flexible, but the neutral order usually puts the verb near the end.

Current sentence:

• Kapı açık olunca sokaktaki gürültüyü duyabiliyorum.

A rough structure is:

• [When the door is open] [the noise in the street] [I can hear]

This is very natural Turkish.

You could also say:

• Sokaktaki gürültüyü kapı açık olunca duyabiliyorum.

This is also grammatical, but it shifts emphasis a bit.

In Turkish, moving parts around often changes focus rather than basic meaning.

Because Turkish verbs usually show the subject clearly.

In duyabiliyorum, the ending -um already tells you the subject is I.

So ben is unnecessary unless you want emphasis or contrast.

• duyabiliyorum = I can hear
• Ben duyabiliyorum = I can hear
  with extra emphasis, like I can hear it

Turkish often drops pronouns when they are obvious from the verb ending.

Yes, but the meaning changes.

• Kapı açık olunca... = when the door is open
• Kapı açılınca... = when the door opens / when the door is opened

So:

• açık olunca describes a state
• açılınca describes an event/process

Your sentence focuses on the state of the door being open, not the moment it opens.

Yes, that is a very helpful literal way to understand it.

• sokakta = in the street
• sokaktaki = that which is in the street
• sokaktaki gürültü = the noise that is in the street

In natural English, we usually say:

• the noise in the street
• the street noise
• the noise from the street

All of those can match the Turkish phrase depending on context.

A rough English-friendly pronunciation would be:

• kah-puh ah-chuk oh-loon-jah so-kahk-tah-kee guer-ool-too-yew doo-yah-bil-ee-yo-room

A few notes:

• ı in kapı is a vowel that does not exist in English; it is not the same as i
• açık has ç like ch
• gürültü has front rounded vowels ü, which are also unfamiliar to many English speakers
• duyabiliyorum is pronounced smoothly, not as separate chunks in real speech

A more Turkish-like syllable breakdown:

• Ka-pı a-çık o-lun-ca so-kak-ta-ki gü-rül-tü-yü du-ya-bi-li-yo-rum

It can be understood either way, depending on context.

Because of duyabiliyorum and the conditional/time phrase, it can mean:

• a general fact: Whenever the door is open, I can hear the noise in the street
• a present situation: When the door is open, I can hear the noise in the street now

Turkish often leaves this kind of distinction to context more than English does.

So this sentence could describe:

• a regular situation
• a present observation
• a practical condition

All are possible.