Важно верить в себя.

Because важно is not an adjective here. It is a predicative adverb/state word used in an impersonal sentence.

Russian often says things like:

• Важно знать. = It is important to know.
• Трудно понять. = It is hard to understand.
• Полезно читать. = It is useful to read.

So Важно верить в себя literally works like It is important to believe in yourself.

If you used важный, that would be an adjective describing a noun, for example:

• важный человек = an important person
• важный вопрос = an important question

Because this is an impersonal construction. Russian very often leaves out the equivalent of English it in sentences like It is important..., It is difficult..., It is necessary...

So:

• Важно верить в себя.
• literally: Important to believe in oneself.
• natural English: It is important to believe in yourself.

Russian does not need a dummy subject like English it here.

Because the sentence is talking about the general action of believing in oneself, not about a specific person doing it right now.

The pattern is:

• Важно + infinitive
• Нужно + infinitive
• Полезно + infinitive

Examples:

• Важно учиться. = It is important to study.
• Нужно работать. = It is necessary to work.
• Полезно отдыхать. = It is useful to rest.

So верить is the infinitive because it means to believe as an idea or action in general.

Because the expression believe in someone / something in Russian is верить в + accusative.

So:

• верить в себя = to believe in yourself
• верить в друга = to believe in a friend
• верить в успех = to believe in success

Without в, верить usually means to believe someone or to trust what someone says, and it takes the dative:

• верить тебе = to believe you / trust you
• верить ему = to believe him

So the preposition changes the meaning.

Here себя is in the accusative case, because it follows в in the meaning believe in.

The reflexive pronoun себя means oneself / yourself / himself / herself / themselves, depending on context.

Its nominative form does not exist, but some of its other forms are:

• себя = genitive / accusative
• себе = dative / prepositional
• собой / собою = instrumental

In верить в себя, the form is accusative.

In an isolated sentence like this, себя is understood generically: oneself / yourself in a general sense.

So Важно верить в себя can mean:

• It is important to believe in yourself
• more generally, It is important to believe in oneself

In real context, себя refers back to whoever the sentence is about.

This is a very common and important question.

• верить в себя = to believe in yourself, to have confidence in yourself
• верить себе = to trust yourself, to trust your own judgment or feelings

So they are related, but not identical.

Examples:

• Нужно верить в себя. = You need to believe in yourself.
• Я не верю себе. = I don’t trust myself.

In your sentence, верить в себя is definitely the self-confidence meaning.

Yes, but the meaning changes slightly because of aspect.

• верить = imperfective
• поверить = perfective

Важно верить в себя means something like:

• it is important to believe in yourself as a general state or ongoing principle

Важно поверить в себя means:

• it is important to come to believe in yourself
• it is important to start believing in yourself / gain that belief

So:

• верить focuses on the ongoing attitude
• поверить focuses on reaching that attitude

Both are correct, but they are not interchangeable in every context.

Yes. Russian word order is flexible, though the neutral order here is very natural:

• Важно верить в себя.

You could also say:

• Верить в себя важно.

This version puts more emphasis on верить в себя. It can sound a little more contrastive or stylistically marked, depending on context.

For a learner, Важно верить в себя is the safest and most standard choice.

Not exactly. Russian does not normally need a word corresponding to English it in this structure.

English says:

• It is important to believe in yourself.

Russian simply says:

• Важно верить в себя.

You may sometimes see Это важно = This is important, but that is a different structure. In your sentence, there is no missing word that needs to be supplied.

The stress is:

• вАжно
• верИть
• в себя́

A simple pronunciation guide:

• Важно ≈ VAZH-na
• верить ≈ vye-REET'
• в себя ≈ f si-BYA

A natural rhythm is:

вАжно верИть в себя́

Also note that в before с is often pronounced more like f because of voicing assimilation, so в себя sounds roughly like f si-BYA.

Yes, very natural. It is a common kind of motivational statement.

Russian often uses this exact pattern:

• Важно помнить... = It is important to remember...
• Важно понимать... = It is important to understand...
• Важно верить в себя. = It is important to believe in yourself.

So this sentence sounds normal, idiomatic, and natural in everyday Russian.