Questions about Harry Potter

[Radagast The Brown]

...that I don't think they deserve their own thread.

As I had nothing to do in the time when my computer didn't work,. I decided to read the books again. And I found many questions... that are unexplained in the books. I'll start with a few:

In the third book, Harry almost killed Black. He threatened him with his wand - but how would he kill him, with a magic? Did he know any magics that kill? Did he have the power to kill someone?

Another question - Why didn;t someone just do the Avada Cadabra spell on Voldemort? Why was it so hard to kill him?

And: How come the tests of a few 'new subjects' were in the same time as old ones? Couldn't someone chose whatever he wanted? How, then, did the tests in Hermione's board were on the same time?