Регистрационный знак можно увидеть на фотографии.

Yes, in this context регистрационный знак is the formal term for a vehicle’s registration plate, which in everyday English is usually license plate or number plate.

A few notes:

• регистрационный = registration
• знак = sign / mark

So the phrase literally means registration sign/mark, but in normal usage it refers to the plate on a vehicle.

In everyday Russian, people also often say:

• номерной знак
• госномер (more colloquial)

So this sentence sounds a bit formal or official.

Because можно creates an impersonal construction.

Можно means something like:

• it is possible
• one can
• you can

Russian often leaves out a subject in this kind of sentence. So Регистрационный знак можно увидеть... literally works like:

• The registration plate is possible to see...
• more naturally: You can see the registration plate...
• or: The registration plate can be seen...

This is very common in Russian.

Because увидеть is perfective, while видеть is imperfective.

Here the perfective verb fits well because it refers to a complete act of seeing or noticing something.

• видеть = to see, to be seeing
• увидеть = to catch sight of, to see successfully, to notice

So:

• можно увидеть = can be seen / can be made out / can be spotted
• можно видеть would sound more like can be seen in the sense of is visible / is observable

Both are possible in some contexts, but увидеть often sounds more natural when talking about spotting a specific object in an image.

It is in the accusative case, because it is the object of увидеть.

However, знак is:

• masculine
• singular
• inanimate

For masculine inanimate nouns, the accusative singular looks exactly like the nominative singular.

So:

• nominative: регистрационный знак
• accusative: регистрационный знак

That is why the form does not change.

Because it is an adjective agreeing with знак.

Знак is:

• masculine
• singular
• inanimate

So the adjective must match it in gender, number, and case:

• регистрационный знак

Since the noun is masculine singular, the adjective takes the masculine singular ending here.

Also, because the noun is inanimate and accusative, the adjective form is the same as nominative:

• nominative: регистрационный знак
• accusative inanimate: регистрационный знак

Russian normally says на фотографии when something appears in a photo.

This is the usual pattern for images and visual surfaces:

• на фотографии = in/on the photograph
• на картинке = in/on the picture
• на экране = on the screen

Even though English usually says in the photo, Russian prefers на here.

So this is something best learned as a normal expression:

• увидеть на фотографии
• быть видным на фотографии
• изображён на фотографии

It is in the prepositional case, because it follows на in the meaning of location.

So:

• фотография = nominative singular
• на фотографии = prepositional singular

This use of на + prepositional answers the question where?

• Где? — на фотографии

The word order can be changed.

Russian word order is more flexible than English word order, because case endings show grammatical roles. For example, you could also say:

• На фотографии можно увидеть регистрационный знак.

Both versions are correct, but the focus changes slightly.

• Регистрационный знак можно увидеть на фотографии.
  This starts with the thing being talked about: the registration plate.
• На фотографии можно увидеть регистрационный знак.
  This starts with the place where it can be seen: in the photograph.

Russian often moves words around to highlight old vs. new information, emphasis, or style.

Not grammatically, no.

In English, the most natural translation may be passive:

• The registration plate can be seen in the photograph.

But in Russian, the structure is actually an impersonal modal construction:

• можно
  • infinitive

So it is not a true passive form. Russian is simply saying that seeing the plate is possible.

A more clearly passive-style Russian sentence would be something like:

• Регистрационный знак виден на фотографии.
• Регистрационный знак может быть увиден на фотографии.

The second one is grammatically possible, but it sounds heavier and less natural.

Yes, in many contexts видно would be very natural.

For example:

• На фотографии видно регистрационный знак.
• more commonly: На фотографии виден регистрационный знак.

These forms mean something like:

• The registration plate is visible in the photograph.

The nuance is slightly different:

• можно увидеть = you can spot it / it can be seen
• видно / виден = it is visible

So можно увидеть focuses more on the act of seeing, while видно / виден focuses more on visibility.

It is singular.

The dictionary form is фотография. After на, in the prepositional singular, it becomes:

• на фотографии

If it were plural, it would be:

• на фотографиях = in/on the photographs

So this sentence refers to one photograph.

Yes, it sounds somewhat neutral-to-formal, mainly because of регистрационный знак.

More casual alternatives might be:

• На фото можно увидеть номер машины.
• На фотографии видно номерной знак.
• На фото виден госномер.

Notes:

• на фото is shorter and more conversational than на фотографии
• номер машины = car number / plate number
• госномер = very common informal way to say license plate number

So the original sentence is perfectly correct, but it has a slightly official or descriptive tone.