Ben dijital fotoğraf makinemle eşsiz anılar kaydediyorum.

That’s true: Turkish often leaves out subject pronouns because the verb ending already shows the person.

• kaydediyorum = I am recording / I record
• So Ben ... kaydediyorum and ... kaydediyorum can both mean I am recording ...

Here, ben is probably included for emphasis or clarity. It can sound like:

• I am recording unique memories with my digital camera.

In many everyday situations, Turkish speakers would simply say:

• Dijital fotoğraf makinemle eşsiz anılar kaydediyorum.

makinemle breaks down into several parts:

• makine = machine
• makinem = my machine
• makinemle = with my machine

So the ending -le / -la means with.

Because the noun already has a possessive ending (-m = my), the -le joins directly onto it:

• makine → makinem → makinemle

In this sentence, it means:

• with my camera

More literally, since fotoğraf makinesi means camera, fotoğraf makinemle means with my photo machine / with my camera.

Turkish very often builds noun phrases by combining words rather than using a completely different single word.

• fotoğraf = photograph
• makine = machine
• fotoğraf makinesi = camera

This literally means something like photograph machine.

When you say my camera, it becomes:

• fotoğraf makinem

The full pattern is based on a Turkish noun compound. The basic dictionary form is:

• fotoğraf makinesi = camera

But when you add my, the ending changes:

• fotoğraf makinem = my camera

So this is normal Turkish structure, not a mistake or an unusual expression.

eşsiz means unique, matchless, or one of a kind.

It comes from:

• eş = equal, counterpart, match
• -siz = without

So literally, eşsiz means something like without an equal.

In this sentence:

• eşsiz anılar = unique memories

It is a strong, positive adjective.

anılar is:

• anı = memory
• anılar = memories

It is plural because the sentence is talking about multiple memories.

It does not have a possessive ending because it means simply unique memories, not my unique memories.

It also does not take the accusative ending here because it is being used as an indefinite direct object. In Turkish:

• bare noun object often = non-specific / general
• accusative-marked object often = specific / definite

So:

• eşsiz anılar kaydediyorum = I am recording unique memories
  (general, indefinite)
• eşsiz anıları kaydediyorum = I am recording the unique memories
  (specific, definite)

kaydediyorum is in the present continuous form, built with -iyor.

Breakdown:

• kaydet- = record
• -iyor = present continuous
• -um = I

So:

• kaydediyorum = I am recording

In Turkish, this form can also sometimes express a habitual action in everyday speech, depending on context. So it may mean:

• I am recording
• or sometimes I record

But the most direct meaning is I am recording.

This is a very common thing that confuses learners.

The dictionary form is:

• kaydetmek = to record

But when a vowel-initial suffix is added, the t often changes to d in pronunciation and spelling in this kind of verb form:

• kaydet-
  • -iyor → kaydediyor

So:

• kaydediyorum = I am recording

This same kind of change appears in some other verbs too. It is something you largely have to get used to as part of the verb’s conjugation pattern.

So the important practical point is:

• dictionary form: kaydetmek
• conjugated form: kaydediyorum

Because Turkish normally uses Subject–Object–Verb word order.

In this sentence:

• Ben = subject
• dijital fotoğraf makinemle = with my digital camera
• eşsiz anılar = object
• kaydediyorum = verb

So the verb naturally comes last.

This is one of the biggest differences from English. English usually says:

• I am recording unique memories with my digital camera.

Turkish naturally says something closer to:

• I, with my digital camera, unique memories am recording.

Even though Turkish word order is somewhat flexible, putting the verb at the end is the most neutral pattern.

Yes, absolutely.

You can say:

• Dijital fotoğraf makinemle eşsiz anılar kaydediyorum.

That is a completely natural sentence.

The ending -um in kaydediyorum already tells us the subject is I. So ben is optional unless you want emphasis, contrast, or extra clarity.

For example:

• Ben kaydediyorum, o silıyor. = I am recording, he/she is deleting.

In a contrast like that, using ben is especially useful.

Yes. The ending -le / -la usually means with.

Instead of using a separate word before the noun, Turkish usually attaches this meaning to the noun itself:

• kalemle = with a pen
• arkadaşımla = with my friend
• makinemle = with my machine / with my camera

So dijital fotoğraf makinemle means:

• with my digital camera

It is functioning like an instrumental/comitative ending.

Because adjectives normally come before the noun they describe in Turkish, just as they do in English.

Here:

• dijital = digital
• fotoğraf makinem = my camera

So:

• dijital fotoğraf makinem = my digital camera

Then adding -le gives:

• dijital fotoğraf makinemle = with my digital camera

So the order is very natural:

• adjective first
• then the noun phrase

It is indefinite.

In Turkish, a direct object without the accusative ending is often indefinite or non-specific:

• anılar kaydediyorum = I am recording memories
• anıları kaydediyorum = I am recording the memories

So eşsiz anılar kaydediyorum means something like:

• I am recording unique memories
• not I am recording the unique memories

This is an important Turkish grammar point, because English does not mark this distinction in the same way.

Turkish allows some word-order flexibility for emphasis.

The neutral version is:

• Ben dijital fotoğraf makinemle eşsiz anılar kaydediyorum.

If you want to emphasize the instrument, you could move that part earlier or stress it in speech. For example:

• Dijital fotoğraf makinemle ben eşsiz anılar kaydediyorum.

But in many cases, natural spoken emphasis is done more through intonation than dramatic word-order changes.

So the original sentence is already good and natural. Word order changes are possible, but the standard version is the safest one for learners.