How to download and install Darwin 13 OS in x86?
The PureDarwin project is attempting to maintain a complete and bootable implementation of the Darwin OS. From their website:


  One current goal of this project is to provide a useful bootable ISO of Darwin 10.x and Darwin 9.x.


Darwin itself is a modified FreeBSD OS with Mach microkernel.

Note though that having Darwin is not a necessary part of developing in Obj-C. Both gcc and clang support Obj-C development in newer versions. You are, of course, limited in what you can do relative to using Obj-C on an OS X machine because there are far fewer standard libraries available outside of the OS X world for Obj-C.