Havoc increases all physical and magical damage (thus excluding true damage). This has nothing to do with AD or AP stats, but just the damage itself. This means that the base damage of an auto attack and ability also benefit from Havoc .
So yes, it also increases the damage for your abilities.
It works in a similar way as to how Rabadon's Deathcap works. It increases your overall attack damage, which, abilities like Broken Wings benefit off of. So...yes.
you said attack damage again. I wanna know if it increases the damage of Pillar of Flame for example. it is " damage " but done with pure ability power.
So yes, it also increases the damage for your abilities.