Таможенную стоимость проверяют в случае если объявленная ценность меняется.

Because it is the direct object of проверяют (check).

The dictionary form is таможенная стоимость. In this sentence, it becomes:

• таможенную — feminine singular accusative
• стоимость — feminine noun; in this pattern it has the same form as nominative, but the whole phrase is still accusative

So Таможенную стоимость проверяют literally means They check the customs value.

This is a very common Russian pattern called an indefinite-personal construction.

Russian often uses 3rd person plural to mean something like:

• they
• people
• officials
• someone in charge

So here проверяют does not mean a specific they. It means something like:

• they check
• it gets checked
• the authorities check it

In English, this is often translated with a passive: The customs value is checked...

A more directly passive Russian version would be: Таможенная стоимость проверяется...

But the active plural проверяют is very normal.

В случае если is a formal way to say:

• if
• in the event that
• in case

It is built from:

• в случае — in the case / in the event
• если — if

So the whole expression introduces a condition.

Compared with plain если, в случае если sounds more official, bureaucratic, or written.

For example:

• Если объявленная ценность меняется... — neutral
• В случае если объявленная ценность меняется... — more formal

Often, yes: many writers prefer в случае, если.

So a more standard edited version would be:

Таможенную стоимость проверяют в случае, если объявленная ценность меняется.

That said, in official or bureaucratic writing you may also see в случае если written without splitting the expression.

For a learner, the safest takeaway is:

• both are understandable
• в случае, если is a very safe written choice

It is a past passive participle used like an adjective.

It comes from the verb объявить — to declare / announce.

So:

• объявленная ценность = declared value

Grammatically, объявленная agrees with ценность:

• feminine
• singular
• nominative

It behaves like an adjective in the sentence, even though it comes from a verb.

This is very common in Russian:

• подписанный документ — signed document
• отправленное письмо — sent letter
• объявленная ценность — declared value

They are related, but they are not exactly the same.

• стоимость usually means price, cost, or monetary value
• ценность usually means worth, value, or sometimes valuable item

In official shipping/postal language, объявленная ценность is a set phrase meaning the value declared by the sender.

In customs language, таможенная стоимость is also a set phrase meaning the value used by customs for assessment.

So the sentence uses two different standard expressions:

• таможенная стоимость — customs value
• объявленная ценность — declared value

A native speaker would understand this difference as terminology, not as random word choice.

Because меняться means to change, while менять means to change something.

Compare:

• Они меняют ценность. — They change the declared value.
• Ценность меняется. — The value changes.

In your sentence, объявленная ценность is the thing that changes, so it is the subject of the verb. That is why Russian uses меняется.

The -ся here often helps make the verb intransitive:

• менять что-то — to change something
• меняться — to change

Not necessarily. In Russian, the present tense is often used for:

• general rules
• procedures
• instructions
• habitual situations

So here:

• проверяют
• меняется

do not mean this is happening right now at this exact moment. They describe a general rule or standard procedure.

English does the same thing sometimes:

• Customs checks the value if the declared value changes.
• The customs value is checked if the declared value changes.

So this is a generic present, not a strictly right now present.

Because it is the subject of меняется.

In the clause:

объявленная ценность меняется

the thing doing the changing is the declared value, so it appears in the nominative:

• объявленная ценность — nominative subject
• меняется — changes

This contrasts with таможенную стоимость, which is the object of проверяют and therefore appears in the accusative.

Yes. Russian word order is flexible, and the sentence can be rearranged for emphasis.

For example:

В случае, если объявленная ценность меняется, таможенную стоимость проверяют.

This version puts the condition first and sounds very natural too.

The original order is also normal, especially in formal writing. Because Russian marks grammatical roles with case endings, the meaning usually stays clear even when the order changes.