For your first spell, there has to be a limit of how many spears you can create and, as only a new student, you cannot have such a powerful ability with the potential to kill; it's too overpowering. We will say that your spears, if they hit, will give 2nd-3rd degree burns along with the instant death of surrounding skin/blood cells. And the maximum amount of spears you can create at a time will be 5 because of this spell's strength. Your other two spells are fine.
Just one more thing, add cooldowns to your spells; using them over and over would be god-modding.