Он верит в судьбу.

• Он = he
• верит = believes
• в = in
• судьбу = fate / destiny in the accusative singular

So the structure is literally He believes in fate.

Верит is the 3rd person singular present tense of the verb верить.

So:

• я верю = I believe
• ты веришь = you believe
• он / она верит = he / she believes
• мы верим = we believe
• вы верите = you believe
• они верят = they believe

In this sentence, он matches верит, so the verb form means he believes.

Because after верить в, Russian uses the accusative case.

The dictionary form is судьба.
Its accusative singular form is судьбу.

This is a very common pattern with feminine nouns ending in -а:

• книга → книгу
• мама → маму
• судьба → судьбу

So:

• верить в судьбу = to believe in fate
• not верить в судьба

Because верить в + accusative means to believe in something — in the sense of believing that it exists, is real, or has power/importance.

This is a fixed and very common Russian pattern:

• верить в Бога = to believe in God
• верить в чудеса = to believe in miracles
• верить в любовь = to believe in love
• верить в судьбу = to believe in fate

So even though в often literally means in, here the whole expression верить в should be learned together as to believe in.

This is a very useful distinction.

• верить в судьбу = to believe in fate
  You believe that fate exists or plays a real role.

• верить судьбе = to trust fate
  You place trust in fate, as if fate will decide things properly.

So the case changes the meaning:

• верить в + accusative = believe in something
• верить + dative = believe someone / trust someone or something

Examples:

• Я верю тебе. = I believe you / I trust you.
• Я верю в тебя. = I believe in you.

That same contrast applies here:

• Он верит в судьбу. = He believes in fate.
• Он верит судьбе. = He trusts fate.

Yes. Russian word order is flexible, although Он верит в судьбу is the most neutral and natural order.

Possible variations:

• Он верит в судьбу. = neutral
• В судьбу он верит. = emphasizes in fate
• Он в судьбу верит. = also possible, often with contrast or emphasis

The basic meaning stays the same, but the emphasis changes.

If you are just learning, the safest default is: Он верит в судьбу.

Sometimes yes, if the subject is already clear from context.

Russian often omits pronouns when they are understood:

• Верит в судьбу. = He/She believes in fate, depending on context

But as a standalone sentence, including он is normal and clear.

So:

• Он верит в судьбу. = full, clear sentence
• Верит в судьбу. = possible in context, but less self-contained

It can often be translated as either fate or destiny, depending on context.

Судьба usually refers to:

• the course of a person’s life
• what is meant to happen
• a larger force that seems to guide events

In many contexts, English fate is the most direct translation.
Sometimes destiny sounds better stylistically.

So in this sentence, the idea is that he believes that life is guided by fate/destiny.

Russian has no articles.

So судьба / судьбу can mean:

• fate
• the fate
• a fate

The exact meaning depends on context.

In Он верит в судьбу, English normally translates this simply as He believes in fate, without an article.

You just change the verb form:

• Он верил в судьбу. = He believed in fate.
• Он будет верить в судьбу. = He will believe in fate.

You may also see the perfective verb поверить, which means to come to believe or to start believing:

• Он поверил в судьбу. = He came to believe in fate.

So:

• верить = to believe, be believing
• поверить = to begin to believe / to believe as a completed change

The stress is:

• Он
• ве́рит
• в
• судьбу́

So: Он ве́рит в судьбу́.

A rough pronunciation guide:

• Он ≈ on
• ве́рит ≈ VYER-it
• в = a short v
• судьбу́ ≈ sood-BYOO

The final word has the stress on the last syllable: судьбу́. This stress pattern is important.