По-твоему, цена высокая?

Because it is an adverbial expression formed in a standard Russian pattern: по- + a pronoun form. In this meaning, it is normally written with a hyphen: по-моему, по-твоему, по-вашему, по-нашему.

Compare that with expressions like по твоему мнению, which are written separately because твоему is modifying a real noun, мнению.

Because this expression uses the dative form of твой. The form твоему is part of the fixed pattern after по- in expressions like по-твоему.

So it is best to learn по-твоему as a whole expression meaning in your opinion.

Because по-твоему is acting like an introductory or parenthetical expression, similar to in your opinion in English. Russian usually separates such expressions with commas.

So these are both possible:

• По-твоему, цена высокая?
• Цена, по-твоему, высокая?

Because Russian normally leaves out the present-tense verb to be. So цена высокая literally looks like price high, but it means the price is high.

This is completely normal in Russian:

• Он дома = He is at home
• Книга интересная = The book is interesting

Because цена is a feminine singular noun, and the adjective has to agree with it. So you get высокая.

A few comparisons:

• цена высокая — feminine singular
• уровень высокий — masculine singular
• зарплаты высокие — plural

In высокая цена, the adjective comes before the noun because it is part of one noun phrase: a high price.

But in цена высокая, the adjective is part of the predicate: the price is high. So here the sentence is not naming a thing; it is saying something about цена.

That is why цена высокая? means Is the price high?, not a high price?

Yes. Цена высока is also correct and means the same basic thing: the price is high.

The difference is style:

• цена высокая sounds more neutral and conversational
• цена высока sounds a bit more formal, concise, or written

For everyday speech, цена высокая is very common.

Yes. Russian word order is flexible, and changing it changes the emphasis more than the core meaning.

For example:

• По-твоему, цена высокая? — emphasis on in your opinion
• Цена, по-твоему, высокая? — emphasis on the price

Both are natural. The first version is especially common when you want to ask for someone’s view.

Yes. По-твоему is informal singular, used with someone you would call ты. По-вашему is used with вы, so it can be:

• polite singular
• plural

So:

• По-твоему, цена высокая? — speaking to one person informally
• По-вашему, цена высокая? — speaking politely or to more than one person

The main stress is:

• по-твОему
• ценА
• высОкая

So the sentence is pronounced roughly as: по-твОему, ценА высОкая?

In speech, the voice usually rises at the end because this is a yes-no question.