Bloody Bullet- Instantaneous damage at a distance, inflicts bleed to all in a radius around the target.
Lancet- Inflicts bleed upon or damages the opponent and heals user over time. For bloodmage, I'd give this a middling cooldown, something like 5 minutes. They seem like they'll be casting from HP a fair bit, so self-healing shouldn't happen often. But I wouldn't rule it out altogether.
First Blood- Damaging skill that does more when the caster's HP is full. AoE? Melee, perhaps? Could inflict bleed upon or just damage the user.
Equalize- think Pain Split from Pokemon. Friendly targets within a radius get their HP added together and redistributed equally with anything above HP caps being lost. So,
User: 100/100, Ally1: 25/75, Ally2: 35/40
100+25+35=160
160/3=53 (and a third)
User: 53/100, Ally1: 53/75, Ally2: 40/40
I'd imagine a large cooldown for this one.