As to whether Moira has deduced that Oliver is hoodie, yes it's technically possible that Moira could have thought Oliver confronted Malcolm in his own person. It's not plausible to me that she would react so calmly to the news her son confronted the villain. Or accept so readily that he got away with it either. Maybe they just muffed her reaction a little in their haste to exposit and move on?
As to why Oliver would continue as hoodie. Merlyn has lost his empire, which means he's lost practically all his power. As for the rest of Merlyn's organization, publishing the book would be more effective now that piles of rubble make it believable evidence. The notion that hoodie can chase Merlyn the Moneyless better than the police tasks willing suspension of disbelief as much as the unfailing abilty of bullets to miss. On the other hand, he gets Laurel if he stays home at nights. (And I do hope that Laurel doesn't suddenly develop a fidelity to Tommy's corpse she didn't feel for the man.)