Fujitora was not allowed to take action. Not just Doflamingo was still a Shichibukai (who the government is willing to let them commit crimes), but Doflamingo blackmailed the Tenryuubito. Fujitora made it very clear how upset he was over the situation.
You just got a character wrong, so there is no helping you. Fujitora stayed passive on purpose. He was taking the casualties into account just to prove that the Shishibukai system is stupid and that the World Gov can be wrong. Of course he could have attacked Doflamingo, but then he couldn't have pulled his show afterwards. He did everything else he could to ensure the citizen's safety, that was his first order on Dressrosa. Also Doflamingo was the World Government King, Riku was deposed and Elizabello technically attacked first since no one remembers he was a toy. Your argument here is completely wrong. As wrong as it could be. Really.
Nope. While I would argue it's well possible that a Shichibukai could do that and the government would turn a blind eye, it's different for Doflamingo. The laws of mortals are irrelevant to gods, and a Tenryuubito can just kidnap a princess of any country and make her a slave. And Doflamingo had persuaded the Tenryuubito to help him on anything.