Can a Djinn Illuminatus make me draw my whole deck with Ancestral Visions?
No, this will not work. You cannot pay the replicate cost that Djinn Illuminatus adds to Ancestral Visions. Ancestral Visions has an unpayable mana cost, and Djinn Illuminatus says


  Each instant and sorcery spell you cast has replicate. The replicate cost is equal to its mana cost.


So, the replicate cost is also unpayable.