I'm having the same problem! DA:I worked fine for me through the shift to Windows 10, but I didn't play for a while, and then had to replace the video card. I can only assume that in some way contributed to it not working now.
I, too, am getting "GetDeviceRemovedReason" errors. They're happening between when I select the initial character options for a new game and when the game itself loads, so I'm not able to save, name the character, or design it.
I've tried the latest drivers and DirectX.
I've tried rolling back the video driver.
I've tried installing the DirectX End-User Runtimes (June 2010) as recommended on several sites.
I've tried putting the game and the Origins client in Compatibility mode for Win 7.
I haven't tried editing the registry yet, because I'm very wary of doing that in Win 10, though I've seen advice that gives instructions for changing Windows 8 settings that might help...
Here's my DxDiag, for what it's worth. I'm currently on the rolled back drivers, but this was recorded before I tried compatibility mode.
https://hastebin.com/ubexozajiw.tex
I'm rapidly becoming convinced that there isn't actually a current solution. I gather it's a problem with the combination of Windows 10, DirectX 12, and games of a certain age, which happens to include DA:I. ☹️
I don't suppose anyone has news?
-E-