Is there a standard us layout for 105 key keyboards, and if so, what is the correct symbol for the key between shift and z?
By definition there is no 105-key U.S. standard, since the U.S. standard (ANSI) defines a 104-key layout.
Different OSes may map the spare key differently, which is probably exactly what you're running into with Cygwin, which probably processes key scan codes itself, rather than receiving parsed characters from Windows. What's also possible is that Cygwin is set to a different keyboard layout altogether (e.g. Windows using U.S. but Cygwin using Swedish).
The closest thing -- by which I mean
really close -- to a 105-key U.S. layout is the U.K. layout, which is designed for ISO keyboards. The main difference is that the added keys are used to add a few punctuation marks and special characters (like £).