How can I convert a Unix path to a Mac OS X path, and the other way?

You can do so using “POSIX file” and “POSIX path”, which can be found in the “Standard Additions” Scripting Addition.

set theUnixPath to "/Users/Shared/"
(POSIX file theUnixPath) as string
--> "Macintosh HD:Users:Shared:"

set theMacOSXPath to "Macintosh HD:Users:Shared:"
POSIX path of theMacOSXPath
--> "/Users/Shared/"