Some are... some aren't. OS X is more of a BSD/NEXT deriritive. There's lots of overlap in terms of similar commands, but there are alot that are proprietary to OS X. You can find a good list here:
Yes they are. Since MacOS X 10.5 Leopard, the operating system has had the full Single Unix Specification certification, meaning it complies with all we normally call "unix". Of course, as JoeyR points out, it still shows its roots from the FreeBSD and NeXTstep worlds.
If you want to compile programs in the traditional Unix fashion, by default MacOS X does not include a gcc compiler. But you can download and install the full XCode SDE for free thru the App Store, just seach for XCode. Beware it is big and will take awhile to download.
For help in specific MacOS X Unix stuff, there is the Mac OS & System Software / Mac OS X Technologies forum.