I at least know that Linux is an OS. However, is Mint a distro of Linux, is it a project? What is Gnome? , are there many different GUI interfaces? Is Linux the base on which I am to learn to build an environment that is comfortable for me, and the end result being a stable environment for me to do my work and to communicate with others using new programs for word processing, video chat and so on?
I apologize in advance for my ignorance?

linux is a kernel that is the basic of what an operating system is (memory management, peripheral management, ...)
gnu is a set of software that make the kernel usable (a shell, gui's, ...)
mint is a distribution which is a grouping of the kernel with various software packages.
gnome is a gui. other gui's include kde, xfce, lxde, fluxbox, ...

for getting your feet wet, i would download a live-usb distribution and install the packages you require thru the package manager.

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Linux is technically just the kernel. All the applications that run on it are called Free Open Source Software (FOSS) and are mostly licensed under the GNU license like the kernel. However in general most people call the OS "Linux".

Linux is a clone of UNIX. There are various commercial variants of UNIX such as Solaris, HP-UX and AIX as well as FOSS versions such as FreeBSD, NetBSD and OpenBSD.

There are multiple distributions (known as "distros) of Linux of which Mint is one. Some of the more popular ones:
Debian
Ubuntu (based on Debian)
RedHat
RedHat Enterprise Linux (a/k/a RHEL commercial version of RedHat)
Fedora (non-commercial distribution derived originally from RedHat but now serves as a test bed for things that later end up in RHEL
CentOS - non-commercial distribution compiled from RHEL source so it looks and acts very much like RHEL.
Slackware
Suse (another commercial distribution)
LFS (Linux from scratch).

There are dozens if not hundreds of distros. Many of the other distros are derived from the ones above. (e.g. kubuntu is a KDE distribution of ubuntu or Scientific Linux and Oracle Enterprise Linux derived from RHEL).

GNOME is a GUI Windows Manager as is KDE and these are the two most popular. There are multiple WMs available including the one that has caused much gnashing of teeth in the Ubuntu community that is a bastar...*ahem*...modification of GNOME.

You can more or less use almost any Linux for testing. If you intend to work on Linux as part of your job you might want to explore CentOS because it will help you learn the most common commercial distro (RHEL). Lots of folks like Ubuntu (or did until they screwed up the WM).

The installation for most distros gives you choices of packages to install and many other packages exist that can be installed after the fact. How to install depends on the distro. However, FOSS software is "open source" which means even if there isn't a prebuilt package for the specific software you want to add to your distro you can typically download the source and compile your own. (LFS is setup so you pretty much compile everything so might be a good one to experiment with just to see where everything comes from.)

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Linux is the kernel

Mint/Ubuntu/Debian/RHEL/CentOS and hundreds of others are distributions of Linux. They use the same fundamental kernel, but the auxiliary programs are different. Different GUIs, different package management systems, etc. When you get down to the core, they all operate basically the same though.

Gnome is one of the GUI window managers (WM) or desktop environments (DE) you can use. KDE is the other kingpin, and then there are many others, some well-known, some not so well known. All these do is provide you a graphical interface to the machine, the programs you actually run are generally the same though. For example, Firefox on Gnome is the same as Firefox on KDE, you just might find the shortcut to it in a different menu. You can install as many DEs as you want on a given system, you just select which one you want to use when you log in to the machine.

You normally don't build your own environment. Most people just choose the distribution they prefer (whichever one has the package management system they like, and is organized the way they like), the DE they prefer (the one that has the menu structure, window switching, etc. that they feel most comfortable with), and then they might make some tweaks here or there so it works exactly how they want (new keyboard shortcuts, etc.)

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One good source of information:
http://distrowatch.com

When talking about GUI interfaces, there are two terms that you will see: "Window manager" and "Desktop environment"---AKA "desktop". For reference, MS-Windows gives you a complete Desktop Environment (There is a window manager built-in and the normal user never sees it.)

In Linux, the most commonly used Desktops are Gnome, KDE, and XFCE. There are several others, and there are also some bare-bones window managers. A strength of Linux--and sometimes an annoyance---is that there are MANY choices.

Start with anything in the top ten on the "hit list" at distrowatch---except Arch. As for the Desktop, you can either flip a coin, or install both. The login manager (AKA display manager will let you choose which to use when you log in.

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Most Linux distros will give you a stable environment, although some feature cutting edge software — the latest versions of programs — which may occasionally spring a nasty surprise. All have software for all the basic activities:
office work: LibreOffice
web browsing: Firefox, Chrome, Opera
email: Thunderbird, Claws, Evolution, Kmail
IRC: Xchat
instant messaging: Pidgin, Kopete
video player: VLC, Dragon, Parole, Totem
There's a good listing of software here: http://linuxappfinder.com

The user interfaces vary a lot. You can try before you install by getting a live disk, which enables you to run the OS and software (a bit slowly!) off the CD/DVD. Good distros for beginners using the various desktops are
KDE (lots of eye-candy): Mepis
Mate (middle of the road): Mint
Xfce (plain and simple): SalineOS
Unity (you either love it or loathe it): Ubuntu

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Back to the terminology issue you raised in your first post.

All distros are projects. Not all projects are distros. Some projects are software packages of various kinds, some small and some large.

Mint would be a project that produces and maintains a distro. Gnome is a project that produces and maintains a desktop environment.

And there are many different desktop environments/window manager. Slackware comes with six by default and you can install others if you wish. I have three on this computer (Gnome, KDE, and Fluxbox--my favorite).

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I'm guessing it is polite to thank everyone that has replied, if not please let me know! Everyone gave me great info and I have a better understanding where I am headed.
Thank you All !

To be completely pedantic - Gnome is a Desktop Environment.
Not exactly. Gnome ain't a Window Manager, it's a DE; the URL above. Gnome, KDE, Xfce - those are DEs. LXDE can be considered a DE to some point but it's actually less than a DE but more than a WM (Window Manager).
As a GUI for GNU/Linux you can use either WM (Window Manager) or DE (Desktop Environment). WM just draws windows and basicly that's about it.
LXDE is when you use kinda both - as a WM it uses OpenBox and adds some extra features and software.

Actually, LXDE is a desktop environment. However, it is less full-featured than GNOME, KDE, or XFCE - not sure how it compares to GNUstep or Enlightenment.

There is no one "best" DE; the choice you face is which DE or which combination of window manager and other accessories provides you with the most comfortable and useful working environment. My recommendation is to try several.