This question is subjective because the answer will differ where you ask (developers, enthusiasts, corporate, etc.). But in my experience most of the Linux users I know prefer the Ubuntu distribution. It is a good choice for casual or serious use because it has a large community of followers and plenty of resources.
Linux
First of all, it's GNU/Linux not just Linux(which is the name of the kernel). Second, most versions of GNU/Linux are free. Lastly, the most popular version is Ubuntu.
Mandrake was a Linux distribution. It later changed its name to Mandriva in 2005, then when it became defunct, a few forks based on it popped up, including:OpenMandrivaPCLinuxOSMageia
No. Red Hat Enterprise Linux is simply a commercial Linux distribution primarily used for servers. It was never a nickname for Linux itself.
There are different types of operating systems. The most popular ones are Microsoft Windows and Linux which is an open- source operating system.
Initially it was just called "Red Hat Linux", but now Red Hat focuses exclusively on the enterprise market with its Linux distribution named "Red Hat Enterprise Linux" (RHEL) with the community version named CentOS (Community ENTerprise Operating System) and Fedora (a Red Hat-supported community Linux distribution)
There are numerous web servers available on Linux, but by far the most popular and most well-supported has to be Apache, which also serves the majority of web sites on the Internet.
Fedora Core and later Fedora !
There is no "the" installation program for Linux. Each distribution has its own (more or less), and it's generally referred to as "the installer" unless they've given it a more specific name.
MicroSoft Windows - Windows 8 : Linux - Ubuntu 14.04 are two examples. Note: Linux is the name of the kernel, while Ubuntu is a distribution (distro) and is one of many Operating Systems available to Linux users for free.
gcc is the most common C-compiler for GNU/Linux platform.
Different Linux distributions can use different GUI's some will use Gnome or KDE. Most distributions will let you choose which you want. If you have an older machine you might want to use XFCE or LXDE window managers. If you are looking for a distribution you might want to try Linux Mint it uses all of these Window Managers.