1) Linux is based on Unix. It was meant to be a free, open-source replacement for Unix, because technically Unix is still a proprietary OS and I think somebody owns it somewhere.
2) The OS X kernel is also based on Unix I believe, either directly or through some other step.
This website looks like it could give you the whole story in minute detail if you are interested.
3) Getting a Mac probably isn't the best way to learn *NIX. Although the kernel itself is based in some version, it's hidden away by the graphics and other prettifying that Apple is known for. I believe you can get down into the kernel if you really want to, but on a Mac, most things are done graphically. If you want to learn *NIX, you need the command line.
Your best option is to simply download a distribution of Linux and install it on a spare PC you have lying around. You don't even have to get rid of Windows; you can dual-boot.