Yes, Singularity uses Docker for its images. This is because most developers around the world prefer using Docker.
No, Singularity is not a popular tool. The ecosystem of Docker is much bigger than Singularity. It is supported by both Windows and Mac integration. But, in the case of singularity, it only has beta mac support and not windows.
Singularity containers are stored in a default cache directory.
No, Docker is not a good choice to containerize HPC workloads.