Close... but wrong terminology
Instead of header files say frameworks. The various frameworks are object oriented libraries that provide access to system resources and common application functionality such as user interface controls, strings, file handling, etc.
The SDK is a development environment with an iPhone emulator, a couple of compilers, an IDE, an Interface Builder and debugger. Think Apple's version of Visual Studio.
Apple Developer Connection is a good place to see tutorials and learn about the OS X specific frameworks as well as Objective C in general.
As the object-oriented portions of Objective-C are essentially the Smalltalk language grafted on top of C, there is not much syntax to learn - Smalltalk has one of the simplest language syntaxes out there.