In Linux/Unix, if I am inside a directory of another user, but cannot view the contents of the directory by typing "ls," how do I get a copy of all the files?
Is the only way to guess what the file names are?
In Linux/Unix, a directory is itself a kind of file that can only be modified by special system calls. Like any other file, access to it is controlled by file permissions.
Looking at it in terms of actually implementation, your question boils down to "how do I read a directory file I can't read?" I'm not making fun of your question — I'm just trying to explain why the answer is a definitive "no".
You need to have super-user priviledges (a.k.a sudo) to do that.
sudo ls /home/Peter/
(if you want to view Peter's files)