Отмена брони возможна без штрафа, если предупредить заранее.

Because возможна agrees with отмена, which is a feminine singular noun.

• отмена = cancellation
• возможна = possible, feminine singular short-form adjective

So the structure is:

• Отмена брони возможна = Cancellation of the booking is possible

If the subject were neuter, you would get возможно. For example:

• Это возможно = This is possible

Here, though, the subject is отмена, so Russian uses возможна.

In the present tense, Russian usually omits to be.

So:

• Отмена брони возможна
  literally looks like: Cancellation of booking possible but means: Cancellation of the booking is possible

This is completely normal in Russian.
If you wanted past or future, then forms of быть would appear:

• Отмена была возможна = Cancellation was possible
• Отмена будет возможна = Cancellation will be possible

Because брони is the genitive singular form of бронь.

Here отмена брони means:

• cancellation of the booking/reservation

Russian often uses the genitive after nouns like отмена to show what is being cancelled.

Compare:

• отмена рейса = cancellation of the flight
• отмена встречи = cancellation of the meeting
• отмена брони = cancellation of the booking

So брони answers the question cancellation of what?

Бронь means booking, reservation, or hold/reservation on something, depending on context.

In travel and hospitality contexts, бронь is a very common word for reservation/booking.

You may also see:

• бронирование = booking, reservation process
• бронь = reservation/booking, often shorter and more everyday

So:

• отмена брони = cancellation of a reservation/booking

Because the preposition без always takes the genitive case.

• без = without
• штраф = penalty, fine, fee
• без штрафа = without a penalty / without a fee

Other examples:

• без сахара = without sugar
• без проблем = without problems
• без паспорта = without a passport

So без штрафа is just standard case government after без.

It can mean both, depending on context.

In everyday Russian, штраф often means a fine or penalty. In hotel, airline, or booking language, без штрафа usually means:

• without penalty
• with no cancellation fee
• free of charge for cancellation

So in this sentence it does not necessarily sound like a criminal or legal fine. It is normal service/business language.

This is a very common compact, impersonal style in Russian, especially in rules, notices, and formal statements.

• если предупредить заранее
  literally: if to notify in advance
• natural meaning: if you notify in advance / if one notifies in advance

It avoids naming a specific subject like вы and sounds more general and official.

A fuller version would be:

• Отмена брони возможна без штрафа, если вы предупредите заранее.

That means basically the same thing, but the original sounds more like a written policy.

Yes, especially in concise, impersonal, or formal language.

It often appears in statements like policies, instructions, or general conditions:

• Если нажать сюда, откроется меню. = If you press here, the menu will open.
• Если прийти раньше, можно занять хорошие места. = If you come earlier, you can get good seats.
• Если предупредить заранее, штрафа не будет. = If you warn in advance, there will be no penalty.

This pattern often has a general meaning like if one does X or if you do X.

Because the sentence refers to a single completed action: giving notice ahead of time.

• предупредить = perfective, to notify / to warn (once, as a completed act)
• предупреждать = imperfective, to be notifying / to notify habitually or repeatedly

Here the idea is:

• if you give notice in advance, then cancellation is possible without penalty

That is a one-time condition, so perfective предупредить fits well.

If you used предупреждать, it would sound more like a repeated or general ongoing practice, which is not the main point here.

Here it means to inform in advance, to give notice, or to let someone know beforehand.

Although предупредить can also mean to warn, in service/hotel/travel contexts it often means:

• to notify
• to inform ahead of time

So in this sentence, it means something like:

• if you let us know in advance
• if you notify in advance

Заранее means in advance, beforehand, or ahead of time.

So:

• предупредить заранее = to notify in advance

It is an adverb, so it modifies the verb предупредить.

You may also hear similar expressions like:

• забронировать заранее = to book in advance
• сказать заранее = to say beforehand
• купить заранее = to buy ahead of time

The word order is natural and clear, but Russian word order is fairly flexible.

This sentence starts with the main topic:

• Отмена брони возможна без штрафа = Cancellation is possible without penalty

Then it adds the condition:

• если предупредить заранее = if notice is given in advance

You could rearrange it in other ways, for example:

• Если предупредить заранее, отмена брони возможна без штрафа.

This version means the same thing, but it foregrounds the condition first.

Because если предупредить заранее is a subordinate conditional clause.

Russian normally separates subordinate clauses with a comma:

• ..., если ... = ..., if ...

So the comma here is standard punctuation.

Yes. The original sounds like written policy language. More conversational versions might be:

• Можно отменить бронь без штрафа, если предупредить заранее.
• Если вы предупредите заранее, можно отменить бронь без штрафа.
• Бронь можно отменить без штрафа, если заранее предупредить.

These all mean roughly the same thing, but the original Отмена брони возможна... sounds especially formal and official.