If you can it sounds like you need to create a new install usb or disk as there is a file missing. You shouldn't be blue screening when installing from USB or disk for that matter. (as you well know) Download Windows 10
The above link is for the windows installation media and it's here you can create a new iso or usb drive.
Create a new install disk or usb and then boot from it making sure you change your boot order via the bios.
Once your into the installation itself you should be given the choice of where to install windows. I always remove which partitions i don't want (basically wipe the c drive) and click next.
Letter assignments are logical, meaning they don't necessarily correspond to the correct physical disk. The lettering is specific to a given boot environment. In your diskpart picture disks and volumes are different things. Disk 0 is your internal hard drive and you should be able to boot to removable media with the Windows installer on it. From a different post you mentioned you ran a clean on the disk. That would have wiped out the partition table so that's why your partitions are missing. Your only option at this point is a clean install.
do you mean by this that you have a normal hard drive as well as the SSD? If so it's simply easier if you disconnect the HDD and just leave the SSD attached. Once you installed you can then attach the HD, may i ask does it have an os on it too?