I have a Nvidia GT 610 graphics card, which does not support Vulkan, but I can perfectly run games on Parallel… Should I use it or should I instead use the Mupen64 core?
Use whichever one you like better. ParaLLEl-N64 includes both and vulkan renderer and an opengl renderer. The opengl renderer uses glide64 plugin by default, while mupen64plus-libretro uses GLideN64 plugin.