Eski cila boya sökücüyle yumuşadı.

It breaks down like this:

• Eski cila = the subject
• boya sökücüyle = an instrumental phrase, meaning with paint remover / using paint remover
• yumuşadı = the verb, softened / became soft

So the structure is basically:

[Subject] + [how/by what means] + [Verb]

This is very natural Turkish word order, especially because Turkish normally puts the verb at the end.

Eski modifies cila.

So:

• eski = old
• cila = polish, varnish, finish, glaze, depending on context

Together, eski cila means old polish/old varnish/the old finish.

In Turkish, adjectives come before the noun, just like in English:

• eski cila = old polish
• yeni boya = new paint

Boya sökücüyle means with paint remover or using paint remover.

It contains:

• boya = paint
• sökücü = remover / stripper / something that removes
• -yle = with, by means of

So:

• boya sökücü = paint remover / paint stripper
• boya sökücüyle = with paint remover

This phrase tells you the means or tool by which the softening happened.

The basic word is ile, which means with.

In everyday Turkish, ile is very often attached to the previous word as a suffix-like form. When that happens, it can become:

• -la / -le
• or -yla / -yle after a vowel

Since sökücü ends in a vowel sound, ile becomes -yle:

• sökücü + ile → sökücüyle

So boya sökücüyle is the natural contracted form of boya sökücü ile.

Both are grammatical, but -yle is much more common in normal speech and writing.

This is a very important difference.

• yumuşadı = became soft / softened
  This is intransitive: the subject itself changes state.
• yumuşattı = softened something
  This is transitive: someone or something causes another thing to become soft.

In this sentence, eski cila is the thing that changed state, so yumuşadı is used:

• Eski cila boya sökücüyle yumuşadı. = The old polish softened with paint remover.

If you wanted to say The paint remover softened the old polish, Turkish would more naturally use a transitive structure, such as:

• Boya sökücü eski cilayı yumuşattı.

So the original sentence focuses on what happened to the polish, not on the remover as the grammatical subject.

Yumuşadı is in the simple past tense.

It can be analyzed as:

• yumuşa- = become soft / soften
• -dı = past tense

And because Turkish does not need a separate word for he/she/it in this kind of sentence, yumuşadı by itself means:

• he softened
• she softened
• it softened
• or more naturally here, it became soft / it softened

In this sentence, it refers to cila, so the meaning is the polish softened.

Turkish does not have articles like English the and a/an.

So cila can mean:

• polish
• the polish
• a polish / a coat of polish

The exact meaning depends on context.

That means Eski cila boya sökücüyle yumuşadı could be understood in English as:

• The old polish softened with paint remover
• An old layer of polish softened with paint remover

English forces you to choose an article, but Turkish often leaves that open unless context makes it specific.

No. They are related to surface finishes, but they are not the same word.

• boya = paint
• cila = polish, varnish, shine coat, finish, glaze, depending on context

So in this sentence:

• cila is the thing that softened
• boya sökücü is the remover/stripper used

Even though boya sökücü literally means paint remover, in real usage it may also be used for removing similar coatings or finishes, depending on context.

Because Turkish normally places the verb last.

So this order is very natural:

• Eski cila = subject
• boya sökücüyle = instrument
• yumuşadı = verb

Turkish word order is more flexible than English, but the verb commonly stays at the end. For example, these are also possible depending on emphasis:

• Boya sökücüyle eski cila yumuşadı.
• Eski cila yumuşadı boya sökücüyle.
  (less neutral, more marked)

The original sentence is a normal, neutral way to say it.

It can often be translated as either, depending on what sounds best in English.

The suffix -yle marks an instrumental meaning, so it can express:

• with
• using
• by means of

So here, all of these are close in meaning:

• The old polish softened with paint remover.
• The old polish softened using paint remover.
• The old polish was softened by means of paint remover.

English chooses among these based on style, but Turkish uses the same instrumental form.

Yes. Turkish usually does not need subject pronouns when the subject is already stated.

Here, eski cila is the subject, so there is no need to add anything like o.

Turkish commonly works like this:

• Eski cila ... yumuşadı. = The old polish ... softened.

Once the noun is present, the sentence is complete. This is very normal in Turkish.