The core information just checks the names for whether it’s “present” or not. If it says it’s present but you’re still missing firmware, that means you have at least one that’s named properly but it isn’t actually the correct file (see the md5 checksums for verification).
You can use a standalone emu if you want, but it’s going to need BIOS images, too. Not to mention that, since it won’t be running through RetroArch, you won’t be able to use any of RetroArch’s features with it.
Beetle-PSX is a lot more accurate (and likewise has higher system requirements) than PCSX-ReARMed, and most of the good qualities of PCSX-ReARMed are only usable on ARM hardware. That is, the super-fast and reasonably accurate renderer requires the ARM NEON SIMD extensions; on x86/64, it falls back to a relatively crummy/buggy/incomplete C version. Ditto for the ARM-only CPU dynarec.