Scarface/WMG

Tony in The World Is Yours can use The World (aka Za Warudo).
Look at the title: The World Is Yours!

Having Dio's time powers would explain all the stuff that he gets to use in Blind Rage. Invincibility is the result of time-locking his physical condition so that none of the damage Tony takes will be fatal. Healing through wounding enemies is extended from Dio's vampirism. The time-locking also explains why reloading a weapon while entering Blind Rage leaves you unable to fire, as opposed to "refreshing" your ammunition count every time it runs low (like in Clive Barker's Jericho): the ammunition status is time-locked at whatever it was at upon entering Blind Rage.

The reason why Tony needs to build his Balls meter is because he does not have mastery over it yet, but give him time.

As for why it does not stop The World around him, maybe Tony prefers to give his enemies the illusion of having a chance. It fits his personality.

Cocaine heals Tony
That's why he can take so much abuse. But TOO much abuse can overwhelm the healing potential.

Scarface is the 1980's version of The Great Gatsby.
To whoever started this header without going into detail, this troper thought of it as the Cliff Notes version of The Godfather