It seems to me that most of your problems within poterm are due to being inexperienced with Unix shells, so I'm not sure that running a live version of Linux will help all that much. Maybe there's a GUI version of unzip, but I don't know myself because I prefer using the command-line.
Like in the Windows shell, there is a PATH environmental variable that denotes which directories are searched for commands. Your problem is that unzip-pro-360+ isn't in any of the command directories in PATH, so it isn't found when you just type the name in. So, you have to specify the exact location of the command when you run it. If it's in the same directory as you're currently sitting in, then adding "./" to the start specifies to the shell that it should look in that directory. So, I would copy both unzip-pro-360+ and the zip file to the root directory via USB, and then in poterm, cd to the /mnt/ext1 directory and run the command as I wrote it above (with "./" in front of the unzip command). The command should be found then, and the contents will be unzipped into the right locations. If you cd somewhere else before unzipping it, then the files will be in the wrong place.