Плата за хранение уже оплачена ввиду того, что таможенное оформление начнётся.

Плата here means a fee or charge — the amount that is due for a service.

So плата за хранение = storage fee.

By contrast:

• оплата = payment, or the act of paying
• платёж = a payment transaction or installment/payment made

So in this sentence, плата is the thing being paid, while оплачена tells you that it has been paid.

Here за means for, as in a fee for storage.

After за in this meaning, Russian normally uses the accusative case:

• плата за хранение = fee for storage
• деньги за работу = money for the work
• оплата за услуги = payment for services

The noun хранение is a neuter inanimate noun, and in the singular its nominative and accusative forms are the same, so it looks unchanged:

• nominative: хранение
• accusative: хранение

So it is accusative here, even though it looks like the dictionary form.

Оплачена is a short passive participle, and it agrees with плата, which is feminine singular.

• плата → feminine singular
• therefore оплачена → feminine singular

Compare:

• счёт оплачен = the bill is paid
• плата оплачена = the fee is paid
• письмо отправлено = the letter is sent

Why not the other forms?

• оплачено would be neuter singular, so it would not agree with плата
• оплатили is an active verb meaning they paid
• была оплачена is also possible, but it sounds more clearly like a past event: was paid / had been paid

Without была, Russian often expresses a present result state, which is why оплачена often corresponds to English has been paid.

Very often, yes.

In sentences like this, short passive participles often describe the current result of an action:

• Плата уже оплачена = The fee has already been paid

It focuses on the present state: the fee is now in a paid status.

If you say была оплачена, that shifts the focus more toward the past action itself:

• Плата уже была оплачена = The fee had already been paid / was already paid

So оплачена here is a very normal choice.

Ввиду того, что means because, since, or more literally in view of the fact that.

It is correct, but it sounds formal, official, or bureaucratic. You are likely to see it in documents, notices, business communication, or legal-style writing.

Less formal alternatives would be:

• потому что
• так как
• поскольку

So this sentence has a somewhat administrative tone.

Because ввиду того, что introduces a subordinate clause.

The part after что is a full clause:

• таможенное оформление начнётся

Russian normally separates this kind of clause with a comma:

• ..., что ...

So the comma is required here.

Начнётся is the future form of the perfective verb начаться.

It means will begin / will start.

This is important because Russian aspect matters:

• начаться = perfective, one completed beginning
• начинаться = imperfective, process / repeated / ongoing beginning

So:

• начнётся = will begin
• начинается = is beginning / begins

In this sentence, the speaker is talking about a future event that will start, so начнётся is the natural form.

Also note: for perfective verbs, what looks like a present-tense form actually has future meaning.

It means customs clearance or customs processing.

Literally:

• таможенное = customs-related
• оформление = processing, formalization, paperwork handling

This is a standard official expression in Russian.

Grammatically:

• оформление is a neuter singular noun
• таможенное is an adjective agreeing with it in gender, number, and case

So the phrase is in the nominative singular here, because it is the subject of начнётся.

Russian often leaves the agent unstated when it is unimportant, obvious from context, or intentionally omitted.

This sentence focuses on the status of the fee:

• the important point is that it has been paid

Not saying who paid it is completely normal in Russian, especially in formal or administrative language.

If needed, Russian could specify the agent, but it often does not.

Yes, Russian word order is fairly flexible.

In:

• Плата за хранение уже оплачена

уже modifies the idea already paid. This is a very natural position.

Other word orders are possible, but they may shift emphasis slightly:

• Уже оплачена плата за хранение — stronger emphasis on the fact that it is already paid
• Плата за хранение оплачена уже — possible, but less neutral in many contexts

The version in your sentence is the most straightforward and neutral.

It is grammatically fine, and in formal Russian this kind of wording is possible.

The idea is something like:

• the storage fee has already been paid in view of the fact that customs clearance is going to begin

So the future event is being treated as an expected or scheduled fact. This is especially natural in bureaucratic or logistical contexts.

A learner may find it slightly unusual because English often prefers a more direct wording. But in Russian official style, this kind of phrasing is not strange.

If someone wanted a less formal or more conversational sentence, they might choose a different connector, but the original is still correct.