Таможенный представитель проверяет документы.

Because таможенный is an adjective, and it has to agree with представитель in gender, number, and case.

Here:

• представитель is masculine
• singular
• nominative case

So the adjective also takes the masculine singular nominative form:

• таможенный представитель = customs representative

The adjective comes from таможня = customs.

Представитель is the subject of the sentence, so it is in the nominative case.

Russian usually puts the doer of the action in the nominative:

• представитель = the representative
• проверяет = checks
• документы = documents

So представитель is the person who is doing the checking.

It is in the accusative. The important thing is that for many inanimate plural nouns, the accusative plural looks exactly the same as the nominative plural.

So:

• nominative plural: документы
• accusative plural: документы

That is normal.

If the noun were animate, the accusative plural would often look different.

Because проверяет is a conjugated present-tense verb, while проверить is the infinitive.

• проверять = to be checking / to check regularly
• проверяет = he/she checks, is checking
• проверить = to check once, to verify completely

In this sentence, you need a finite verb meaning checks / is checking, so проверяет is correct.

Проверяет is imperfective.

The imperfective verb is:

• проверять

Its present-tense forms describe:

• an ongoing action
• a repeated action
• a general process

So проверяет документы can mean:

• is checking the documents
• checks documents

If you wanted a future meaning with the perfective verb, you would use:

• проверит = will check / will have checked

Mostly from the case endings, not just from word order.

In this sentence:

• представитель is nominative, so it is the subject
• документы is accusative plural, so it is the object

The neutral word order here is:

• Таможенный представитель проверяет документы.

But Russian can reorder this for emphasis:

• Документы проверяет таможенный представитель.

That still means The customs representative checks the documents, but the focus shifts toward documents.

No. Russian has no articles.

So таможенный представитель could mean:

• a customs representative
• the customs representative

Which one is meant depends on context.

The same is true for документы:

• documents
• the documents
• sometimes even some documents, depending on context

It can be both.

Literally, it means:

• customs representative

But in real-world usage, it can also refer to a specific professional or legal role in customs procedures, depending on context.

So a learner should understand it first as a normal noun phrase:

• таможенный = customs
• представитель = representative

Then later, in official or business contexts, it may function almost like a set term.

The main stress is:

• тамо́женный представитель проверя́ет докуме́нты

A rough pronunciation guide:

• тамо́женный ≈ ta-MO-zhen-nyy
• представи́тель ≈ preet-sta-VEE-tyel'
• проверя́ет ≈ pra-vye-RYA-yet
• докуме́нты ≈ da-ku-MEN-ty

A couple of useful notes:

• Unstressed o often sounds closer to a
• The -тель ending in представитель has a soft ль
• Russian stress is very important and must be learned with each word

Yes. In many contexts, документы can be translated naturally as:

• documents
• papers
• ID and paperwork
• documents/papers

For example, at a border or customs checkpoint, English speakers might naturally say:

• The customs officer is checking the papers.

So even if the dictionary meaning is documents, the best English translation can vary by situation.

In normal Russian, descriptive adjectives usually come before the noun:

• таможенный представитель

That is the standard order.

Putting the adjective after the noun is generally not the normal neutral pattern in modern Russian prose. In some special styles, fixed expressions, or emphatic constructions, word order can vary, but for everyday learning you should treat adjective + noun as the standard rule here.

Проверяет is:

• 3rd person
• singular
• present tense
• imperfective

So it means:

• he checks
• she checks
• it checks
• or, in context, is checking

Russian present-tense verbs do not usually show gender, so проверяет could refer to a male or female representative. You understand that from context, not from the verb ending.