In order to read or write /proc/pid/mem your process needs to be allowed to ptrace() the target process. You can’t do that for arbitrary processes. Similar story for WriteProcessMemory().
Above your security context, no, but you can definitely WriteProcessMemory any other process that is in your same security context or lower (something similar holds for ptrace, although remember that SUID/SGID binaries are running not at a same security context)
