I've just finished reading through Functional Decision Theory: A New Theory of Rationality, but there are some rather basic questions that are left unanswered since it focused on comparing it to Casual Decision Theory and Evidential Decision Theory:

• How is Functional Decision Theory different from Timeless Decision Theory? All I can gather is that FDT intervenes on the mathematical function, rather than on the agent. What problems does it solve that TDT can't? (Apparently it solves Mechanical Blackmail with an imperfect predictor and so it should also be able to solve Counterfactual Mugging?)
• How is it different from Updateless decision theory? What's the simplest problem in which they give different results?
• Functional Decision Theory seems to require counterpossibilities, where we imagine that a function output a result that is different from what it outputs. It further says that this is a problem that isn't yet solved. What approaches have been tried so far? Further, what are some key problems within this space?