Can you run Unix and linux programs on mac os x

You can't use Linux binaries on OS X.
However most Linux apps are available in source code and you can compile many of them on OS X out of the box, or with minor porting efforts.
There are several projects out there like Fink or the FreeBSD ports system, that provide already ported apps in source code.
Also many Apps, like XFree86 or the GIMP! are available as OS X binaries.
Getting the XFree Binaries from and fink from worked pretty well for me to get most of the apps I used to use on Linux to my OS X Desktop, YMMV.