You're welcome. Glad I could help.
From the list, most of those functions are implemented in libc, but overridden in Noux. Please note that Noux provides a system call interface, while libc doesn't normally use or require that, but instead uses Genode's library function calls more directly. The execve function isn't implemented except in Noux AFAIK, but could possibly be implemented without a special environment.
First, if you haven't already, you should follow the instructions for creating a build directory, then build and run one of the many scenarios, e.g. run/demo.
For compiling a simple C application, you first need to have/pick a repos subdirectory. To start out, you could use one of the ones provided, e.g. repos/gems. You then need to create a subdirectory for your application somewhere inside repos/[your repo]/src, e.g. repos/gems/app/simple_c_app. After that, you need to write your C code and place it in a file in that directory. Then write a makefile named
target.mk in the same directory with the C code. The makefile should look something like the following:
TARGET = simple_c_app
SRC_C = main.c
LIBS = base libc posix
When you have your source file(s) and makefile written, and your repo directory added to etc/build.conf in your build directory, you should be able to compile it using "make app/simple_c_app".
If you want to run your app, you need to write a run script. Creating a good run script for testing your app might be difficult, but you can start with something simple. You can start by copying repos/gems/run/pipe.run and modifying that.
For most of this, I'd recommend looking at the pipe example by Emery Hemingway, as found in repos/gems/src/app/pipe, and the aforementioned run script. Please note that the pipe example uses C-style C++. If you want to use pure C, be sure to use the variable SRC_C in the makefile rather than SRC_CC.
I hope this helps.