1. Definitely maybe. A .tar.gz file is most likely source code, which might well be able to compile on OSX - you'd have to check whether the program works on various unix platforms. If it works on FreeBSD, your chances are likely pretty good.
Advice - try fink first. It will handle programs that depend on a zillion libraries that you don't have, and download and install all of them first.
2. I'm not quite sure what you mean - a unix terminal is no use without a unix OS to run on. You would have a nice rectangle on the screen, but no commands you could run.
OS X consists of a bunch of (closed source) graphical apps, running on the (open source) Darwin operating system. Darwin, in turn, consists of a FreeBSD user environment, with some considerable modifications by Apple, running on the Carnegie Mellon University's Mach microkernel.
So, yes, the operating system itself is heavily based on FreeBSD.