Цена весьма высокая.

In Russian, the verb to be is normally omitted in the present tense.

So:

• Цена весьма высокая. = The price is quite high.

There is no present-tense word corresponding to English is here. This is completely normal Russian.

In the past or future, Russian does use forms of to be:

• Цена была весьма высокой. = The price was quite high.
• Цена будет весьма высокой. = The price will be quite high.

Because it must agree with цена.

The noun цена is:

• feminine
• singular
• nominative

So the adjective also has to be:

• feminine
• singular
• nominative

That gives:

• masculine: высокий
• feminine: высокая
• neuter: высокое
• plural: высокие

So:

• высокая цена = a high price
• цена высокая = the price is high

Both цена and высокая are in the nominative case.

• цена is the subject
• высокая is the predicate adjective describing the subject

This is a very common pattern in Russian:

• Дом большой. = The house is big.
• Погода хорошая. = The weather is good.
• Цена высокая. = The price is high.

Весьма means something like:

• quite
• rather
• very
• considerably

The exact translation depends on context and tone.

In this sentence, Цена весьма высокая suggests something like:

• The price is quite high
• The price is rather high

A useful thing to know: весьма sounds a bit more formal or bookish than очень.

Compare:

• Цена очень высокая. = neutral, everyday
• Цена весьма высокая. = more formal, polished, sometimes slightly literary

Yes.
Цена очень высокая is perfectly natural and probably more common in everyday speech.

Compare the tone:

• очень = the standard everyday word for very
• весьма = more formal, refined, or written

So both are correct, but they do not sound exactly the same stylistically.

Yes, basically the same idea.

Russian says:

• высокая цена = high price
• низкая цена = low price

So this works very much like English:

• Цена высокая. = The price is high.
• Цена низкая. = The price is low.

This is a normal and standard way to talk about prices.

Yes, you could. That uses the short form adjective:

• высокая = full form
• высока = short form

So both are possible:

• Цена весьма высокая
• Цена весьма высока

The difference is mostly stylistic:

• высокая sounds more neutral and common in modern speech
• высока sounds a bit more formal, concise, or bookish

For many learners, the full form высокая is the safer everyday choice.

No, Russian word order is fairly flexible, but changing it can change the focus or emphasis.

Neutral statement:

• Цена весьма высокая. = The price is quite high.

Other possibilities:

• Весьма высокая цена. = A rather high price / Quite a high price
  This is now a noun phrase, not quite the same sentence structure.
• Высокая цена. = A high price
• Цена высокая. = The price is high

So the original order is natural and straightforward for a full statement.

Russian has no articles.

So цена can mean:

• the price
• a price

Which one is meant depends on the context.

In this sentence, English usually translates it as the price is quite high, but Russian itself does not mark that distinction with an article.

A simple learner-friendly pronunciation guide is:

• це-на́
• весь-ма́
• вы-со́-ка-я

Main stresses:

• цена́
• весьма́
• высо́кая

Very rough English-style approximation:

• tsy-na
• vyes-MA
• vy-SO-ka-ya

A few notes:

• ц sounds like ts
• stressed syllables are important in Russian
• unstressed vowels are often reduced in actual speech

Yes, but with a small note about style.

• Цена высокая. = very natural, neutral
• Цена очень высокая. = very natural, common
• Цена весьма высокая. = natural, but a bit more formal or polished

So the sentence is correct and natural, but весьма gives it a slightly more formal tone than ordinary conversation often has.