"Can I make a code that saves information just like a login but with two files in the same directory?"
Yes, but this makes no sense since you suggest "file 1" should contain the user and password details, "file 2" contains this with the addition of the stage. Why have two files when "file 2" contains all of this data? This is the only question I can find in your post. I suggest you think about your design some more and read How do I post a question effectively?. If you have any questions quesitons please feel free to ask.
"Also I heard Perl isn't much for games so if this isn't possible"
Your question has nothing specific to computer games, you're asking about basic file input and output.