I don't understand your question 1. Are you asking why the "function library" pane on the left does not contain some of the functions that might be suggested to you through tool tips while you type? If so, as far as I know, the documentation is sometimes not catching up with the changes in RobotC. For me, I would consult with the code. There is a file called RobotCIntrinsics.c in the folder "C:\Program Files (x86)\Robomatter Inc\ROBOTC Development Environment\Includes". This file contains all the intrinsic functions supported by RobotC. Since this is code, it must be up-to-date with respect to the RobotC versions you have.
There are several aspects for your question 2. First, RobotC is not standard ANSI C. For example, although it supports pointers since 3.x, it still doesn't support function pointers. Also, RobotC support some C++ features such as function overloading, parameter initialization etc, however, it doesn't support class. In other words, it is not an Object-Oriented-Programming language.
Regarding your question on variable initialization, it depends on what kind of variable you are talking about? Even for other compilers such as Microsoft Visual C/C++, only global variables are zero initialized because they are created at compile time in the data segment. For local variables in the functions, they are stack variables that got dynamically created when the function is called. These variables are not usually initialized (even in Visual C/C++).
Regarding your question on the function exit(), there is no "built-in" functions in the C/C++ language spec. So in general, the compiler does not really know about functions such as exit() or even printf(). Functions are provided by the "run-time library". And yes, there is a "Standard ANSI C runtime library" that people are used to and love but for C/C++ languages specifically designed for a certain platform and environment (such as in embedded environment or robotics), there is no obligation to support the whole ANSI C runtime library. Many platforms prefer to support some but not all of the standard C runtime library functions. Like I said, check out the RobotCIntrinsic.c file and you will see all the functions supported by it.
Hope that answers all your questions.