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.
1. Not everyone is rich enough to buy flaghship phones.
2. Lots of gamers just use XBox or PS4 (no Vulkan there). And on PC, not everyone uses Steam. Plus Microsoft already started to be more agressive regarding games on Windows 10, with Age of Empires remaster being the first example.
3. Well it is a matter of taste, not everyone craves for FPS, then there is also the small matter that Vulkan is not supported on XBox anyway, while DX 12 is. With much better developer tooling.