Eh, not for WebGL it won't. Nobody even implements DX other than high-powered desktop GPUs.
Will it live on? Sure, we will still have games and Xboxes. But if you're going to pick a standard that can work on mobile and desktop, there is no contender other than Vulkan.
2. Both of them... If you are gamer, you are going to Steam (and Valve is not a friend of the Windows store idea). I'm not happy with this situation either, as I prefer GoG, and GoG is a distant second.
3. Doom, Wolfenstein II, F1 2017, The Talos Principle from the other side of genre spectrum or the upcoming Star Citizen. Vice versa is more true, there's no DX12 game worth playing, that's not also Vulkan game.