No it can't be downloaded from Blizzard website. Try downloading it from Direct2drive or Steam.
I added a link below to a download site. I hope it works!
The Diablo 2 Patch can be downloaded from Blizzard's website under Diablo 2 Updates. However they no longer send out patches for Diablo 2 because they no longer make sales from the game.
Blizzard
You simply download it from a website but it is against the rules of blizzard to use. If one is caught with it you will be banned from battle.net.
The full game is not available for (legal) download, but Blizzard did put out a demo version that allowed you to play the first few levels of the dungeon.
No, Diablo I has nothing to do with Diablo II.
No. There are Diablo 3 teaser videos on the Blizzard website.
Blizzard Entertainment
Download diablo hacks
There is a Diablo 3.
Blizzard Entertainment
Just open the game with the internet on and it should download automatically. Blizzard is like Steam, it will download the updates when needed every time you start the game.