Can Ubuntu run Mac OS X?
I currently run Windows 7 – can I download and run one of the OS X programs?
No, Ubuntu cannot run Mac OS X, neither legally nor technically. An OS can not run an OS. Your Ubuntu PC technically could, but Apple's EULA states OS X can only be installed on Apple machines.
As for running Mac programs on Windows 7, again this is a no. You can run some of them on Linux. Linux is Unix-like, and OS X is UNIX-certified, so some things can work.