Separate multiple sequence into different file, one sequence per file
There's an app for that! The exonerate package (see here) includes a nice fastaexplode command that does exactly what you're looking for and will be much, much faster than anything we give you here since it is written in C and not a scripting language. Just install exonerate (you can do that with sudo apt install exonerate on Debian-based systems) and then:

fastaexplode file.fa


This will create these two files (file.fa is the original input file from your question):

$ ls
file.fa  KQK14546.fa  KQK21959.fa