Gece lambasını kapatmadan uyuyamıyorum; başucumdaki suyu da her gece yeniliyorum.

Kapatmadan means without turning off or without closing.

It comes from:

• kapatmak = to turn off, shut, close
• -madan / -meden = without doing

So:

• kapatmadan = without turning off
• gece lambasını kapatmadan = without turning off the night lamp

This -madan / -meden form is very common in Turkish for without doing X.

Because gece lambası is a Turkish noun compound meaning night lamp / night light.

In this type of compound:

• the first noun describes
• the second noun usually takes a compound ending

So:

• gece = night
• lamba = lamp
• gece lambası = night lamp / night light

That -sı in lambası is not really showing possession like his/her lamp here. It is the normal form of this compound.

Then, because the phrase is the direct object of the verb and refers to a specific lamp, it becomes:

• gece lambasını

So the full structure is:

• gece lambası = night lamp
• gece lambasını = the night lamp

They both have the accusative case, which is used for specific direct objects.

Here the speaker is talking about:

• a specific night lamp
• a specific glass/container of water by the bedside

So:

• gece lambası → gece lambasını
• su → suyu

In Turkish, compare:

• su içiyorum = I drink water
  (water in general, non-specific)
• suyu içiyorum = I drink the water
  (specific water)

So in this sentence, lambasını and suyu both mean that particular thing, not just any lamp or any water.

Because uyuyamıyorum means I can’t sleep, while uyumuyorum means I’m not sleeping or I don’t sleep.

That is a big difference.

• uyumuyorum = I am not sleeping
• uyuyamıyorum = I am unable to sleep / I can’t sleep

So the sentence is not saying the speaker simply does not sleep. It says the speaker is not able to sleep unless the lamp is turned off.

This is a very common Turkish pattern for inability.

It is built from the verb uyumak = to sleep.

A useful way to understand it is:

• uyu- = sleep
• ability/inability pattern = can / cannot
• -yor = present continuous
• -um = I

So uyuyamıyorum means:

• I am not able to sleep
• more naturally in English: I can’t sleep

You do not need to memorize every tiny sound change at first; the important thing is to recognize -amıyor / -emiyor as a very common pattern meaning cannot / am not able to.

Başucumdaki means the one at my bedside or the one by my pillow/headside.

It can be broken down like this:

• baş ucu / başucu = bedside, the area by one’s head
• başucum = my bedside
• başucumda = at my bedside
• başucumdaki = the one that is at my bedside

Then:

• başucumdaki su = the water at my bedside
• başucumdaki suyu = the water at my bedside (as a specific direct object)

The ending -ki is very useful in Turkish. It turns a location-based phrase into something adjective-like:

• masadaki kitap = the book on the table
• odadaki kişi = the person in the room
• başucumdaki su = the water at my bedside

Because this da means also / too, and that word is written separately in Turkish.

So:

• suyu da = the water too / also the water

This is different from the locative ending -da / -de, which is attached to the word:

• evde = at home
• masada = on the table

So:

• başucumda = at my bedside
  (-da attached: location)
• suyu da = the water too
  (da separate: also)

Here yeniliyorum means something like:

• I replace it
• I refresh it
• I make it fresh again

The verb yenilemek often means to renew or replace with a fresh/new one.

So başucumdaki suyu her gece yeniliyorum means the speaker changes the bedside water every night, probably replacing it with fresh water.

Yes, this is understandable and natural. Depending on style, Turkish speakers might also say things like:

• değiştiriyorum = I change/replace it
• tazeliyorum = I freshen it

But yeniliyorum works well here.

Because those two uses of gece do different jobs.

• gece lambası = a kind of lamp, a night lamp/night light
• her gece = every night, telling you when the action happens

So the first gece is part of a noun, while the second gece is a time expression.

They are not repetitive in function.

Yes, this word order is natural.

Turkish usually puts the verb near the end, so this structure is very typical:

• Gece lambasını kapatmadan → background/action before the main verb
• uyuyamıyorum → main verb
• başucumdaki suyu da her gece → object + also + time
• yeniliyorum → main verb

A more literal layout would be:

• Without turning off the night lamp, I can’t sleep; the water at my bedside, too, I replace every night.

Turkish word order is flexible, so some parts could move for emphasis, but the version in your sentence sounds normal and idiomatic.

For example, her gece could move:

• Başucumdaki suyu da her gece yeniliyorum
• Her gece başucumdaki suyu da yeniliyorum

Both are possible, with slightly different emphasis.

Yes. In Turkish, kapatmak is often used for both ideas, depending on the object.

For example:

• kapıyı kapatmak = to close the door
• televizyonu kapatmak = to turn off the TV
• lambayı kapatmak = to turn off the lamp

So in gece lambasını kapatmadan, the meaning is clearly without turning off the night lamp, not without closing the night lamp.