Can a user mode fault cause a Blue Screen of Death (BSOD)? Is it possible that a memory access violation like double freeing memory can cause a blue screen or only a kernel mode exception (like a driver exception) cause Windows to crash?
Not directly.
Direct fault will cause an exception and program crash. To cause a BSOD, the user mode application must communicate either directly or indirectly with a kernel mode driver that is possible not robust enough to protect itself from invalid user mode input.