Why was Draco Malfoy chosen to try to destroy Albus Dumbledore?

Maybe it's because Belatrix Lestrange talked to Voldemort about it.  Voldemort decided if he didn't do this, he would kill Draco and his family.

http://inthecapital.com/2012/08/23/draco-malfoy-chooses-towson-over-hogwarts/#ss__24564_1_0__ss

Why did death give the first brother the elder wand?

Death pretended to greet the three brothers.  The first brother said he wanted the most powerful wand ever made.

Why did Draco Malfoy disarm Dumbledore?

He disarmed him because he was told to by Lord Voldemort.

Why did Dumbledore go to Tom Riddle to talk to him about coming to Hogwarts?

Dumbledore wanted to make Tom Riddle a better person, and he knew that Tom could do magic.  He could tell that Tom Riddle had evil thoughts, but Dumbledore gave Tom Riddle another chance.

How did the mirror of Erised become property of Hogwarts?

It might have been the property of one of the four founders of Hogwarts, but no one really knows.  The mirror of Erised shows you what you want, and the one who looks into this mirror will only see himself exactly as he is.

How many wands did Voldemort use?

Tom Riddle (Voldemort) only had one wand of his own.  He stole four wands during his life to do evil things.  The picture above shows one of the wands that Voldemort used to try to kill Harry Potter.

Why did Hagrid bring Aragog (the spider) into the dark forest to live?

Tom Riddle framed Hagrid and the spider for killing people at Hogwarts.  Really it was the basilisk, and Tom Riddle was controlling it.  Hagrid helped Aragog to escape.