So, should he level up Chaos, walk around with that artifact, and damage his own units? What about mana? And will it even affect the hero? Should he immediately go for Alt Golems? And how does BDP make a mage overpowered?

Why damage his own units? Only yellow golems are placed on the battlefield.
Academics have the highest Knowledge stat, so do they really have mana problems? If random chance causes problems, nothing prevents taking artifacts and skills that boost mana and Knowledge. And on Random Maps, I often have a mana well.
You can search online (and there are even videos) about how to achieve Utopia in 1-2 weeks using BDP. And it's easier for mages to do this - in a shorter time, they can deal more damage than non-magic factions, thanks to powerful spells.

With BDP, we survive longer, which means we can cast more spells.