Madara is a god of death.
Therefore, he has a Death Note.
how did he get it? well, with MS, you can learn to summon the Note. Something he didn't teach Itachi, I guess.
by killing his brother and getting his "eyes", he gains the "shinigami eyes", and is able to see a person's name by looking at their face. with his absurdly fast seal-making speed, NOTHING could stop him writing a name.
what's more, he gained the abilities of a shinigami as well. he can pass through walls, or let attacks slide through him.
he can also live for an insanely long time, because he increases his life span by killing others.
Shodaime investigated Madara, who wanted to create a "perfect world" with only good people. Shodaime argued that it wasn't in his hands to do that, and they started to bicker over matters of the village. Shodaime managed to defeat him by discovering his secret, and secretly destroying his Note, before he could write his name down. Unfortunately, the Note has a 1-per-person rule, so Madara was left relatively powerless. He was then banished. Luckily though, he had killed enough people to extend his life span a LONG TIME.
i'm not sure about the tailed beasts, though. maybe they can make a new Note?
shinigami like apples. Madara likes apples. Therefore, Madara is a shinigami.
Shodaime's never wanted to reveal his name. you need the person's name to kill them. do the math.
and for those of you who haven't realized yet, this is a........never mind.
madara can fly. really really high. if that's not a shinigami characteristic, then I don't know what is.
madara actually means light, and uchiha is another spelling of yagami.....go figure.