At one point in the manga, Kaname tells Zero: "I envy you, you who can protect the girl you love". People at that point naturally assumed he meant how Zero was able to directly protect Yuuki while he wasn't. Then in chapter 61 and beyond we're introduced to Kaname's past where he knew a mysterious pureblood woman who ended up sacrificing herself for the creation of hunters. Kaname reveals how he was the one supposed to have sacrificed himself instead and is shown mourning her memory in some occasions, implying she was the woman he thought of when telling Zero what he did, not Yuuki.
Kaname somehow feels a need to lock Yuuki in their home in the second arc to keep her from danger, even though purebloods can't die, or are very difficult to kill.
Justified as its later shown that there are weapons that even untrained humans can use to kill pureblood. Not to mention the frequent political jockeying and quarreling in vampire society where even the lower nobles would take advantage of a moment of weakness to kill a pureblood as Ouri suffered.
A vampire hunter is ambushed by a pureblood at a ball early in the second arc, even though vampire hunters are supposed to be able to detect vampires from long distances. Similarily, neither Yuuki or Zero seem to know Aido is spying on them at one point. Purebloods can also sense each other, however Kaname still seem unaware that Yuuki is just standing a few feet away from him while she's evasdropping on a conversation between him and Kaien.
Remember the only vampire hunters in action are the badass ones (in this case, the cream of the crop such as Zero). Much like any organization, not everyone is a fighter; in real life even the special forces have operators part of the team who don't do fighting and are out of shape. Not to mentioned even among frontline troops, not everyone is a 007 Bond or an Audie Murphy and all have varying levels of skillset. The vampire hunter killed is a typical grunt and it was a pureblood, someone even Kaname has trouble with, who did the killing. AS for eavesdropping, I'd chalk it up to Zero not being in 100% alert and too busy distracted at the moment (such as Yuki's drama instances). It is shown that in times of unprepared mental state of minds such as being exhausted from lack of drinking blood that even purebloods are in a vulnerable position and vampires don't necessarily use their superhuman powers every moment of consciousness as seen in Adou's flirty moments.
There's apparently a huge amount of level E vampires as implied in the second arc, however only a few purebloods exist, and none of them are said to turn humans for fun, leaving the question as to where all those level E's come from.
Some of them may have existed for centuries. As the story later reveals, the purebloods are often trying to use every chance to do crime when they can get away with it. Its just the purebloods hold too much political power for a direct investigation especially when evidence is not conclusive.
At the end, it's revealed that Kaname had been working on a cure that transforms vampires into humans. In that case, why didn't he continue with that instead of going on a genocide mission that ended up in a Motive Decay?
A combination of more important matters at hand, the extreme difficulty of the research as Adou attest, and Science Marches ON implying that Kaname lacked the necessary technology and medical science to make advances when he stopped (which Adoui also confirms when he stated he had to blend in modern knowledge with the stuff Kaname discovered to create a base to start from).
How does Yuuki know the human spell won't eventually break for Kaname, who was possibly the most powerful pureblood and vampire in general, when it broke for a weak pureblood like her?
Keep in mind Yuki is gambling on Kaname's affection for her to help in convincing him to stop or at least provide enough delaying time.