Её волнует цена.

Because in this sentence, she/her is not the subject. The subject is цена (the price).

Russian uses волновать in a pattern like:

• Что-то волнует кого-то
• Something worries someone

So:

• цена = the thing causing the emotion
• её = the person affected by it

That is why Russian uses её (her) rather than она (she).

Because цена is the subject of the sentence — the thing that is doing the worrying.

A very literal breakdown is:

• Её = her
• волнует = worries
• цена = the price

So the structure is essentially:

The price worries her.

Since цена is the subject, it stays in the nominative.

Here её is accusative.

The verb волновать normally takes the person affected in the accusative case:

• Меня волнует... = ...worries me
• Тебя волнует... = ...worries you
• Её волнует... = ...worries her

One thing that can confuse learners is that её can look the same in different cases. In this sentence, it is functioning as accusative.

Because it agrees with цена, which is singular feminine.

Russian verbs in the present tense agree with the subject in number (and in the past tense also gender). Here the subject is:

• цена = singular

So the verb is singular:

• волнует

If the subject were plural, the verb would be plural too:

• Её волнуют цены.
  Prices worry her.

A very literal translation is:

Her worries the price → more naturally in English: The price worries her.

This is useful because many English speakers want to say something like She worries about the price, but Russian often expresses it the other way around with волновать:

• Её волнует цена.
• literally: The price worries her
• naturally: She is worried about the price / The price concerns her

They are related, but they work differently:

• волновать = to worry / disturb / concern someone
• волноваться = to worry / be nervous / get worried

Compare:

• Её волнует цена.
  The price worries/concerns her.

• Она волнуется из-за цены.
  She is worried because of the price.

So:

• волновать focuses on what causes the worry
• волноваться focuses on the person's state

Both are common, but the grammar is different.

Yes. That is a very natural alternative.

The difference is mainly in structure and emphasis:

• Её волнует цена.
  The price concerns/worries her.
  Focuses on the price as the issue.

• Она волнуется из-за цены.
  She is worried about the price.
  Focuses more on her emotional state.

Both can be appropriate depending on context.

Yes. Russian word order is flexible.

You can say:

• Её волнует цена.
• Цена её волнует.

Both are grammatically correct, but the emphasis changes.

• Её волнует цена can sound like a neutral statement.
• Цена её волнует puts more focus on цена — as if contrasting it with other things.

Russian often uses word order to show topic and emphasis, not just grammatical roles.

Not necessarily.

Волновать can mean:

• to worry
• to trouble
• to concern
• to affect emotionally
• sometimes even to excite / stir emotionally, depending on context

In Её волнует цена, the most natural sense is usually:

• The price concerns her
• She is worried about the price

So it does not always mean panic or deep anxiety. It can also mean that something is an important concern.

Mostly yes, but one important detail is ё.

• её is pronounced roughly yi-YO
• the ё is always stressed

In everyday writing, Russians often replace ё with е, so you may see:

• ее instead of её

But the pronunciation is still её, not a flat ее.

Because this verb uses a direct object pattern instead.

In English, we often say:

• She worries about the price

But Russian can express the same idea through:

• Её волнует цена
  literally: The price worries her

So instead of worry about + something, Russian often uses:

• something worries someone

That is why there is no preposition here.

No. In this sentence, её does not mean her in the possessive sense.

Here it means her as an object pronoun:

• Её волнует цена = The price worries her

If you wanted her price, you would usually need context showing that её is possessive, for example:

• Её цена слишком высокая.
  Her/its price is too high.

So in your sentence, the structure clearly shows that её is the person affected by the verb.

You can swap её for other accusative pronouns:

• Меня волнует цена. = The price worries me.
• Тебя волнует цена. = The price worries you.
• Его волнует цена. = The price worries him.
• Нас волнует цена. = The price worries us.
• Их волнует цена. = The price worries them.

This is a very useful sentence pattern to learn:

Кого волнует что?
What worries whom?