Перерасчёт начнётся при условии, что ошибка в начислении подтверждена.

Перерасчёт means recalculation or adjustment after recalculation. It is a common administrative/billing word.

It is built from:

• расчёт = calculation
• prefix пере- = re-, again

So in contexts like utilities, salary, benefits, or billing, перерасчёт often means that the amount will be calculated again because something was wrong the first time.

Начнётся is the future form of the perfective verb начаться = to begin / to start.

Russian uses the perfective here because the sentence is talking about the start of the recalculation as a single event:

• перерасчёт начнётся = the recalculation will begin

Compare:

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

In this sentence, the future one-time event is what matters, so начнётся is the natural choice.

При условии, что means provided that, on condition that, or if in a formal sense.

It is more formal and bureaucratic than plain если.

So:

• при условии, что ошибка подтверждена = provided that the error is confirmed

You often see при условии, что in official notices, contracts, instructions, and customer-service language.

There is a comma because что introduces a subordinate clause.

The structure is:

• main clause: Перерасчёт начнётся
• subordinate clause: что ошибка в начислении подтверждена

Russian normally separates this kind of clause with a comma:

• при условии, что ...

Also, при условии, что functions as a set conjunction, and the comma is standard here.

Ошибка is nominative because it is the subject of the subordinate clause:

• ошибка ... подтверждена = the error is confirmed

But в начислении follows the preposition в, so начисление has to be in the prepositional case:

• в начислении = in the billing / in the charge / in the accrual

So the grammar is:

• ошибка = subject
• в начислении = prepositional phrase modifying ошибка

In everyday Russian, начисление is a fairly technical or administrative word. In this kind of sentence, it usually means something like:

• a charge
• an accrued amount
• a billed amount
• a posted payment/fee

So ошибка в начислении is an error in the billed amount or error in the charge/accrual.

The most natural English translation depends on context:

• utilities: billing error
• salary/benefits: error in начисление may be more like payroll/accrual error
• taxes/fees: assessment/calculation error

Подтверждена is a short-form passive participle, and here it is used as the predicate:

• ошибка подтверждена = the error is confirmed / has been confirmed

This is different from:

• подтверждённая ошибка = a confirmed error
  
  • here подтверждённая is the full form and works like an adjective before a noun
• ошибка подтверждается = the error is being confirmed / gets confirmed / is confirmed
  
  • this is a verb form and has a different nuance

In official Russian, short passive participles like подтверждена are very common.

Because it agrees with ошибка, which is:

• feminine
• singular

So the short passive participle must also be feminine singular:

• ошибка подтверждена

Compare:

• факт подтверждён = the fact is confirmed
• заявка подтверждена = the application is confirmed
• данные подтверждены = the data are confirmed

Russian normally leaves out the present-tense form of to be.

So:

• ошибка подтверждена literally has no separate word for is
• but it means the error is confirmed or the error has been confirmed

This is normal Russian grammar.

If you wanted past or future, Russian would show it:

• ошибка была подтверждена = the error was confirmed
• ошибка будет подтверждена = the error will be confirmed

It can often mean either, depending on context.

In practice, this short passive participle often expresses a resulting state:

• the confirmation has already happened
• and now the error stands as confirmed

So in English, depending on style and context, you might understand it as:

• the error is confirmed
• the error has been confirmed

In this sentence, the idea is that recalculation will start only once the error has been officially verified.

Yes, but it would sound less formal.

For example:

• Перерасчёт начнётся, если ошибка в начислении подтверждена.

That is understandable, but the original with при условии, что sounds more official and written.

A slightly more explicit future version would be:

• Перерасчёт начнётся, если ошибка в начислении будет подтверждена.

That version makes the future timing clearer. The original sentence is more concise and bureaucratic in style.

Yes. Russian word order is flexible.

You can also say:

• При условии, что ошибка в начислении подтверждена, перерасчёт начнётся.

This means the same thing. The difference is mainly emphasis:

• original order starts with the main result: the recalculation will begin
• reversed order starts with the condition first

Both are grammatically correct, especially in formal written Russian.