Vincente Valtieri is the gang vampire. He's the most obvious vampire in the game and is quite kind to you. Since he's your first guy to award quests he always gives you helpful advice.
A Watery Grave
You've got to kill a pirate on-board his ship, but luckily its docked. There's no bonus for this quest, so go at night while he's sleeping. Go to the Waterfront district of the Imperial city, where there should be two ships, The Floating Bloat (a clever bar title) and the pirate's ship. Walk on-board the pirate ship and go into sneak mode. Jump up on the rail above the crate on the top part of the ship and look down. The back of the ship houses a balcony, the door of course leads to the Captain's quarters. If you can manage, pick the lock, it will be very hard. Once in, the captain should be asleep in his bed a few feet away. Stay in stealth mode, grab the Nirnroot if you wish, and stab him in the back a few times. When he's dead loot the corpse and quickly and get off the boat through the balcony door. If you don't, the pirates of the ship will come to see what's going on, if you're there when they breach the door, you'll have an unnecessary fight on your hands.
A man needs to be killed but it has to look like an accident. If you make it look like an accident, you'll be rewarded nicely. Vincente suggests to you that loosening the Minotaur head above the victims chair as he sits in it will fulfill the bonus nicely, but if you kill the target's butler, Gromm, you'll lose the bonus. Make sure you have a few lockpicks and head over to to Bruma. The best time to go into the house is late night, between 2-5am, while everyone one is sleeping and no one is watching. This will help you avoid Gromm as well.
Break into his house while in stealth mode. Inside the house, remain in shadow and head up stairs. In one of the two bedrooms there will be a portion of wall that you can open and enter a small passage way. Head to the end and wait until 8pm-11pm, when he's in his chair, and undo the knotting, listen as it falls and kills him. Since its an "accident", Gromm won't attack you. Sneak out of the house just in case. Head back to the Sanctuary to turn in. Vincente will give you your money as well as Sufferthorn if you made it look like an accident and didn't kill Gromm. He'll also promote you to Slayer!
Scheduled for Execution
Now, you know you've been thinking about it since the first minutes of the game, killing that insulting Dark Elf in the cell across from yours. When that secret passage opened up you thought to yourself "One day when I'm powerful I will come back through here and kill him!" Now is your chance, and you get paid to boot. Vincente gives you a key that will get you back into the sewers you made your first escape from, while also informing you that if no guards are killed in the process, you will receive a bonus.
Head back in, you'll find it full of guards. Really, they probably only need one or two guards stationed at the entrance, but since its not guarded, your entrance is easy. Inside, follow the tunnel to a set of stairs, picking the lock at the top of the ladder ladder you see. From here, you hear two guards conversing about why they are stuck down there patrolling the sewage system. If you have an invisibility spell or potion, use it and head up to the next room, otherwise, wait for the two guards to finish their whining. If you're able, try and steal a key from a guard.
In the next room, full of plenty of shadow, a single guard will be patrolling, watch his pattern and sneak by when you feel most comfortable. if you feel really comfortable, and didn't grab a key off the other two guards, try and snag his. Follow your quest marker through all the corridors within, until you reach a path leading up to a hole in a wall, you should hear another guard talking. He's actually conversing with your target, that blasted Dark Elf. Luckily you're armed this time, and back in your first prison cell. Wait for a moment and listen to the Dark Elf's crazy dreams of escape and glory. Wait for the guard to leave, open your door, you can mess with him a little if it satisfies you, then shoot a couple arrows through the bars at him.
If you managed to grab a key off one of the patrolling guards below, head up the stairs and walk out of the prison. Head back to Vincente for your reward of 100 gold and The Scales of Pitless Justice, if no guards were killed. Still can't believe you got paid for that, can you?
The Assassinated Man
When you're assigned the quest, Vincente gives you a poison dagger and the antidote, you're going to fake murder someone. Meet up with the "victim", Francois, he'll ask you to wait for the other person that will assassinate him to show up. As the assassin appears, stab Francois with the poison dagger. The other assassin will try to kill you now, so run out of the house and get out of town. If the assassin dies at the hands of the guard, you won't receive the reward.
Once you've shook the assassin, head back to town and sleep/wait for about a day. When you wake up, go to the basement of the chapel and give Francois the antidote. He'll mention that this is his family's tomb and that they will see this as desecration, making an attack inevitable. Just as he says this, zombies will attack, kill them off or flee, it doesn't really matter. Escort Francois to the inn and talk to him. Now head back to Vincente for your reward, Cruelty's Heart a Necklace, and your promotion Eliminator.