Коль скоро заявку на участие приняли, регистрационный взнос оплачен.

In this sentence, коль скоро is a bookish/formal connector meaning something like since, given that, if indeed, or once depending on context.

Here it introduces the first clause as the condition/background for the second one:

• Коль скоро заявку на участие приняли, ... = Since / given that the application was accepted, ...

So it is not a basic everyday phrase like если or раз. It sounds more formal, written, and slightly old-fashioned.

Not very. A native speaker will understand it, but it sounds noticeably formal, literary, or bureaucratic.

In everyday speech, people are more likely to say:

• если
• раз
• поскольку
• раз уж

So a more everyday version might be something like:

• Раз заявку на участие приняли, регистрационный взнос оплачен.

That said, the original sentence is perfectly understandable; it just has an official/written flavor.

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

Russian often uses 3rd person plural when the doer is unknown, unimportant, or obvious from context:

• приняли = they accepted
• but in English we often translate it as a passive:
  • the application was accepted

So:

• заявку на участие приняли

literally means:

• they accepted the application for participation

but idiomatically in English it is often:

• the application for participation was accepted

Russian does this a lot:

• Меня пригласили = I was invited
• Документы проверили = The documents were checked

Because приняли is the perfective past form of принять, and it shows a completed action.

Compare:

• принимали = were accepting / used to accept / accepted in a process-like sense
• приняли = accepted, finished accepting

Here the sentence refers to a completed result: the application has already been accepted. That completed action fits well with the result in the second clause:

• регистрационный взнос оплачен = the fee is paid / has been paid

So the whole sentence is about completed outcomes, not an ongoing process.

Заявку is the accusative singular of заявка, because it is the direct object of приняли:

• приняли что? → заявку

The phrase на участие means for participation and modifies заявку:

• заявка на участие = application for participation

So the whole phrase means:

• the application to participate
• or more literally, the application for participation

As for участие: after на in this expression, Russian uses the accusative form. But участие is a neuter noun whose nominative and accusative singular look the same, so the form does not visibly change.

Оплачен is the short passive participle of оплатить.

It means:

• paid
• has been paid
• is paid

depending on context.

So:

• регистрационный взнос оплачен

means:

• the registration fee has been paid
• or the registration fee is paid

This is a very common formal Russian pattern, especially in written or administrative language.

Compare:

• Счёт оплачен = The bill has been paid
• Заказ оформлен = The order has been processed
• Документы подготовлены = The documents have been prepared

Because заплатили would focus more on the action and the people who did it, while оплачен focuses on the resulting state.

Compare:

• Регистрационный взнос заплатили = They paid the registration fee
• Регистрационный взнос оплачен = The registration fee has been paid / is paid

The version with оплачен is more formal and impersonal. It sounds very natural in official notices, systems, and administrative texts.

Russian normally omits the verb to be in the present tense.

So:

• регистрационный взнос оплачен

literally behaves like:

• the registration fee [is] paid

That is why there is no есть.

As for был:

• был оплачен would clearly place the statement in the past: was paid
• оплачен without был usually presents the current resulting state: is paid / has been paid

So the sentence is not missing a word; it is using a normal Russian pattern.

The comma separates the clause introduced by коль скоро from the main clause.

Structure:

• Коль скоро заявку на участие приняли,
  subordinate/background clause
• регистрационный взнос оплачен.
  main statement

So the comma works much like in English:

• Since the application was accepted, the registration fee has been paid.

Russian normally uses a comma before or after subordinate clauses like this.

Yes, very much so.

Several things create that tone:

• коль скоро is bookish/formal
• заявка на участие is administrative vocabulary
• регистрационный взнос is official terminology
• оплачен is a formal result-state construction

So this does not sound like casual conversation. It sounds more like something from:

• a form
• an official notice
• internal documentation
• a registration system
• formal correspondence

Yes. Russian word order is flexible, though different orders may sound more or less natural depending on style and emphasis.

For example, you could also say:

• Коль скоро приняли заявку на участие, регистрационный взнос оплачен.

The original order:

• заявку на участие приняли

puts the object before the verb, which is perfectly normal in Russian, especially in formal or written style.

So the word order here is not strange; it just reflects Russian flexibility and a slightly formal presentation.