The second one is correct according to the rules of the 2nd conditional...past tense and would. "when" can be substituted and used instead of "if"

The first one is correct. It implies that the teacher had faith in their student and believed she or he would grow up to become "the next Bill Gates". The second sentence implies that the teacher is a time-traveler of some sort; traveled into the future, found out their student becomes "the next Bill Gates", went back in their time, and informed the student of the situation; so now the student also knows they will become "the next Bill Gates" for sure. Such certainty and confidence in saying such a thing is only reserved for close family, in my opinion! A teacher is supposed to be a more rational and realistic character, not go around turning their students into swellheads. So, to recap, using "will" in the sentence shows the teacher simply has faith in the student's abilities, whereas using "would" indicates the teacher is a time-traveler and is 100% sure their student will become "the next Bill Gates". Letting you know, I'm not a native English speaker but I've studied the language for 7 years and I'm still practicing it.

It's in the past, so you use would. Never use will in a sentence describing the past. You use will for reported speech in the past, because you are reporting exactly what was said. It's not part of the sentence proper, it follows its own grammar rules. My teacher said "you will be the next Bill Gates."

I think will is correct. Because your teacher knew you and he/she was sure that you were a clever student.