wǒ xiāngxìn nǐ huì chénggōng.

You normally cannot say 我相信你成功 in this context; it sounds incomplete or wrong.
To talk about a future result, you need something like:

• 我相信你会成功。 – I believe you will succeed.
• 我相信你一定会成功。 – I believe you will definitely succeed.

Without 会 (or another marker like 一定, 能够, etc.), the sentence doesn’t sound natural for this meaning.

In this sentence, 成功 functions as a verb meaning “to succeed”.
So the basic structure is:

• 我 (subject) – 相信 (verb) – 你会成功 (object clause “that you will succeed”).

成功 can also be a noun (“success”), but here it’s used as “to succeed”, not “success” as a thing.

Chinese doesn’t use a separate word like English “to” before verbs in this way.
The idea of “to + verb” is just expressed by the verb itself:

• 你会成功 = “you will succeed” (not “you will to succeed”).
  So 成功 already covers “to succeed” without needing an extra marker.

是 is generally used to link nouns or noun phrases (A is B), not a subject directly to a verb phrase.
You can’t say 我是相信你会成功 as a normal equivalent of “I believe you will succeed”; it sounds wrong or at least very odd.
The correct pattern is simply:

• 我相信…… – I believe that …

是 is not needed before another main verb like 相信.

• 我相信你 = “I trust you / I believe in you” in a general sense (your character, abilities, honesty).
• 我相信你会成功 = “I believe you will succeed”, focusing on a specific outcome in the future.

You can also say both together for emphasis:
我相信你，我相信你会成功。 – I believe in you; I believe you will succeed.

我相信你 by itself is already a common and natural way to say “I believe in you”.
If you want to connect it more explicitly to success, you can say:

• 我相信你，一定会成功。 – I believe in you; (you) will definitely succeed.
• 我相信你会成功。 – I believe you will succeed.

For strong encouragement, many speakers add 一定 (“definitely”).

You could say 我相信你能成功, and it’s acceptable, but the nuance is slightly different:

• 会成功 – more about a future outcome / likelihood: “will succeed.”
• 能成功 – more about ability or possibility: “can manage to succeed,” “are capable of succeeding.”

可以成功 is less common and sounds a bit more like “it is possible for you to succeed,” not as natural in encouragement as 会成功 or 能成功.
For the standard encouraging sentence, 会成功 is most natural.

You can simply reverse the roles and add 吗:

• 你相信我会成功吗？ – Do you believe I will succeed?

Structure: 你 (you) + 相信 (believe) + 我会成功 (I will succeed) + 吗 (question particle).

You place 不 before 相信:

• 我不相信你会成功。 – I don’t believe you will succeed.

The pattern is: 我 + 不 + 相信 + (clause).
You do not negate 会 here; you negate the act of believing.

In this context:

• 相信 – “to believe / have faith in / trust”, often with a feeling of confidence or trust.
• 觉得 – “to feel / to think” in a subjective, casual way (often about impressions or feelings).
• 认为 – “to consider / to hold the opinion that”, more formal or logical.

For encouraging someone about their success, 相信 is the most natural choice:
我相信你会成功。 sounds warmer and more supportive than 我觉得你会成功 or 我认为你会成功.

Yes, both are very common to emphasize certainty and encouragement. Typical positions:

• 我相信你一定会成功。 – I believe you will definitely succeed.
• 我相信你肯定会成功。 – I believe you will surely / definitely succeed.

They go before 会, modifying the degree of certainty about the future event 成功.

• 相 (xiāng) – 1st tone (high and level). Don’t let it fall.

• 信 (xìn) – 4th tone (sharp falling).
  Together: 相信 – high level + sharp fall.

• 成 (chéng) – officially 2nd tone, but often sounds like a light rising from mid to high.
• 功 (gōng) – 1st tone (high and level).

Practice the rhythm of the whole sentence:
wǒ xiāngxìn nǐ huì chénggōng – try to keep the tones clear and the sentence smooth and even.