Well, take it from the perspective of a school. The whole point of the academy's existence is to train fine Gatekeepers, with the fate of both worlds in their hands. Why would they want unlawful individuals in a team to kill monsters, as they would be a liability. I'm not the CS acceptor, but I'm offering advice.
As for start day, will be tomorrow most likely.
I appreciate it, but it doesn't help much. First was a Lawful Evil character that was utterly denied for reasons still yet explained to me. The other so far is being rejected because it upsets the "taste" of some GMs.
I haven't created a character yet, but I have discussed with the other GMs about your character.
Since you want a concrete answer, I shall give you several on why pretty much ALL the gms said no. Not just some.
I'll start with the most glaring issue. Your power is OP.ANYONE with blood will already lose.. since he can just pretty much drain,mind control, and flippin make weapons from their own blood. I fail to see how this really is balanced at all. There's really only one character, the machine that would be able to really do anything against him. I also do not see how you would limit this power at all, since it's concept makes it utterly broken for anyone who has blood.
Now, you might say, look at his weaknesses. We've looked at them, and they really do not justify allowing "blood sorcery". First of all, a mage with light or dark magic would simply get destroyed by "blood sorcery." Sunlight is almost irrelevant as it does not affect him that much. And it doesn't help that the only side effect from overuse is going berserk. Secondly, that "weakness" also means that in any major battle, he'd attack allies and enemy alike, since there would be immense bloodshed.
Your lore is also flawed. If they were born of some legendary dragon who pretty much pissed off everyone, I don't see why he would be allowed in a school that is about protecting others, since he also has that world domination gig going on. Your lore has no indication that vampires would really be a friendly group either, leading to issues of coexistence. His goals will not be achieved by going to this Academy, which again, is about peace between both worlds as well. Even if he was discreet about his goals, there's still that.
These reasons are mainly why no gm has allowed your CS. It's not a matter of taste, it's a matter of a broken power and the lore you have established has broken the lore of AoTTA. As for your other CS, I have not seen it, so I cannot make any judgement on that one.