I use clang or gcc.
iirc, clang comes with the Apple command line tools which you can download from the Apple developer website.
If not, you can install it via macports (which is akin to linux's apt-get). You want to make sure you have the latest versions (clang 3.3, or gcc 4.8) in order to get the latest C++11 updates.
The compiler interprets your program into well.. A program. It transforms your source code into machine code for the computer to execute.
The IDE (stands for Integrated Development Environment) is a glorified text editor. It provides facilities to compile your program or step through line by line and debug your program. An IDE is not required. You can code in TextEdit if you want.
Loosely. Notepad++ is more of a text editor.
Does notepad++ offer the feature to compile your program from inside Notepad++? If so, i would say yes. IDE. Otherwise, text editor.