How can I specify a drive in Applescript without the drive name?
Instead of using HFS file paths, use posix paths.
Use System Events for file operations, which handles posix paths as well as HFS paths.  It even knows how to expand the ~, so your home directory can be expressed simply as folder &quot;~/&quot;, and your main disk is mounted at folder &quot;/&quot;.
As for your attached USB drives, you essentially have to reference them by name.  They'll be listed under folder &quot;/Volumes&quot;, or you can use this command (via System Events):
get the name of every disk where it is ejectable -- i.e. attached drives

I'm not entirely able to tell if I've answered all your questions.  Leave a comment and I'll fill in whatever seems missing.