Gece sessiz olunca daha rahat uyuyabiliyorum.

Here gece means at night / when it is night.

In Turkish, many time words can be used without a case ending to mean during that time:

• sabah = in the morning
• akşam = in the evening
• gece = at night

So gece here is not just a dictionary-style night. In this sentence, it functions like a time expression: at night.

You could think of the beginning as:

• Gece ... = At night, ...

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

• sessizken = when it is quiet / while it is quiet
• sessiz olunca = literally when it becomes quiet, but very often it is also used in the broader sense of when it is quiet

In everyday Turkish, olunca is extremely common for expressing a condition or situation that happens and then leads to a result.

So:

• Gece sessizken daha rahat uyuyabiliyorum.
• Gece sessiz olunca daha rahat uyuyabiliyorum.

Both are natural.
The version with olunca can sound a bit more like when the night is quiet / once things are quiet at night.

The suffix -ınca / -ince / -unca / -ünce often means:

• when
• once
• sometimes if in a general, repeated-situation sense

Here:

• olmak = to be, to become, to happen
• olunca = when it is / when it becomes / once it is

So:

• sessiz olunca = when it is quiet or more literally
• when it becomes quiet

This structure is very common in Turkish:

• eve gelince = when he/she comes home
• yorgun olunca = when one is tired
• zaman olunca = when there is time

That is a very common learner question, because olmak is a very flexible verb.

It can mean things like:

• to become
• to be
• to happen
• to occur
• to take place

In combinations with adjectives, Turkish often uses olmak where English might simply use be.

For example:

• hazır olmak = to be ready
• iyi olmak = to be well / to get well
• sessiz olmak = to be quiet

So sessiz olunca is perfectly natural Turkish for when it is quiet.

Daha usually means more, and rahat means comfortable, relaxed, easily depending on context.

So daha rahat means:

• more comfortably
• more easily
• with more comfort

In this sentence, English would usually say:

• I can sleep more comfortably
• I can sleep more easily

Even though rahat is often taught as an adjective, it is also very commonly used in ways that correspond to an adverb in English.

Uyuyabiliyorum is made of several parts:

• uyu- = sleep
• -y- = a linking consonant
• -abil- = can / be able to
• -iyor = present continuous / current ability
• -um = I

So:

• uyu + y + abil + iyor + um
• uyuyabiliyorum
• I can sleep

In this sentence, because of daha rahat, it becomes:

• I can sleep more easily / more comfortably

The extra y appears for pronunciation and word connection.

The verb stem is uyu-, which already ends in a vowel.
When Turkish adds another vowel-starting suffix, it often inserts y as a buffer consonant.

So instead of something awkward like uyuabiliyorum, Turkish says:

• uyuyabiliyorum

This is very normal:

• anla-y-abilirim = I can understand
• başla-y-ınca = when it starts
• uyu-y-abilirim = I can sleep

The form -Abil- expresses ability/possibility: can, be able to.

When combined with -iyor, it often describes a current/general ability in real situations.

So uyuyabiliyorum means:

• I can sleep
• I am able to sleep
• in context, I manage to sleep

It does not mean that the speaker is sleeping right now.
It means the speaker has that ability under those conditions.

Compare:

• Uyuyorum. = I am sleeping.
• Uyuyabiliyorum. = I can sleep / I am able to sleep.

Because Turkish verb endings already show the subject.

Here, -um at the end of uyuyabiliyorum tells you the subject is I.

So ben is optional.

• Uyuyabiliyorum. = I can sleep.
• Ben uyuyabiliyorum. = I can sleep.
  (with extra emphasis on I)

Turkish often leaves subject pronouns out unless they are needed for contrast, emphasis, or clarity.

Here it is closest to when.

The sentence expresses a general pattern:

• When the night is quiet, I can sleep more comfortably.

But in Turkish, -ınca/-ince can sometimes feel a bit broader than English when and may overlap with a repeated-condition sense like whenever or even if in some contexts.

In this sentence, the idea is:

• whenever the night is quiet, the result is that I sleep more comfortably

So the best understanding is:

• when / whenever

Yes, that is a possible literal reading.

Because olunca comes from olmak, a more word-for-word version could be:

• When the night becomes quiet, I can sleep more comfortably.

But in natural English, most people would say:

• When it’s quiet at night, I can sleep more comfortably.
• When the night is quiet, I can sleep more easily.

So the literal structure and the natural English translation are slightly different.

These forms are related but not the same.

• uyuyorum = I am sleeping
• uyurum = I sleep / I can sleep / I usually sleep depending on context
• uyuyabiliyorum = I can sleep / I am able to sleep

In this sentence, uyuyabiliyorum is important because the meaning is about ability or ease under certain conditions.

So:

• Gece sessiz olunca daha rahat uyuyorum.
  = When it is quiet at night, I sleep more comfortably.
• Gece sessiz olunca daha rahat uyuyabiliyorum.
  = When it is quiet at night, I can sleep more comfortably.

The second one suggests that quiet makes sleeping possible or easier for the speaker.

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

The given sentence is natural:

• Gece sessiz olunca daha rahat uyuyabiliyorum.

You could also say:

• Gece sessiz olunca uyuyabiliyorum daha rahat.
• Daha rahat uyuyabiliyorum gece sessiz olunca.

But these alternatives may sound more marked or conversational, with different emphasis.

The most neutral structure is:

• condition first: Gece sessiz olunca
• result after: daha rahat uyuyabiliyorum

That pattern is very common in Turkish.

Yes, you could, and it would be understandable and natural.

Compare:

• sessiz olunca
• sessiz olduğunda

Both can mean when it is quiet.

Very roughly:

• olunca is often a bit lighter, more everyday, and very common in speech
• olduğunda can sound a bit more explicit or slightly more formal/written

In many everyday situations, the difference is small.

So both are fine:

• Gece sessiz olunca daha rahat uyuyabiliyorum.
• Gece sessiz olduğunda daha rahat uyuyabiliyorum.

In Turkish, words like rahat can function in ways that cover what English separates into adjective and adverb usage.

• rahat bir yatak = a comfortable bed
  Here it acts like an adjective.
• rahat uyumak = to sleep comfortably / easily
  Here it corresponds to an adverb in English.

So in this sentence, rahat modifies the way the sleeping happens:

• daha rahat uyuyabiliyorum = I can sleep more comfortably / more easily

Turkish does not always need a special -ly-type form the way English does.

A comma is optional here.

You may see:

• Gece sessiz olunca daha rahat uyuyabiliyorum.

or

• Gece sessiz olunca, daha rahat uyuyabiliyorum.

Both are acceptable.
In short Turkish sentences like this, people often leave the comma out.
The meaning does not change.