If I buy Diablo 3 (which I intend to do) and bind it to this very same Battle.Net account, will we be able, my friend an I, to run these two games at the same time on different computers?

You can log into Starcraft 2, Diablo III, and all 8 of your World of Warcraft accounts at the sametime if you wanted at.

Of course sharing your account with your friend is a horrible idea, him knowing your password means he can access your account anytime he wants, I suggest logging in for him.

Sharing your account of course is against the Terms of Service.

Or should I create another Battle.Net account and prey for Blizzard to leave me the hell alone and not asking for an official identification on the rare occasions I connect to the two different Battle.Net accounts with the same IP?

There is no reason to do this.

If I buy Diablo 3 (which I intend to do) and bind it to this very same Battle.Net account, will we be able, my friend an I, to run these two games at the same time on different computers?

You can log into Starcraft 2, Diablo III, and all 8 of your World of Warcraft accounts at the sametime if you wanted at.

Of course sharing your account with your friend is a horrible idea, him knowing your password means he can access your account anytime he wants, I suggest logging in for him.

Sharing your account of course is against the Terms of Service.

Or should I create another Battle.Net account and prey for Blizzard to leave me the hell alone and not asking for an official identification on the rare occasions I connect to the two different Battle.Net accounts with the same IP?

There is no reason to do this.