I am writing code with a program called Microsoft Visual C++ Express.
Do not bother, upgrade to "Microsoft Visual Studios Community" immediately. It is basically the entire Microsoft Visual Studios Professional 2013 except completely free. No this is not a scam, Microsoft plans to replace Express with Community to encourage Microsoft platform development. You can even make fully commercial products with it without paying them!
The catch is the licence is for personal use and small businesses only. As such there are still catches (larger companies still need to buy licences) however you get what you pay for and having the entire MSVS 2013 free of charge for personal use or small business is one of the best value offers I have ever seen MS make.
1.) What is a "Framework".
Generally a collection of abstract classes or utility methods. The framework itself does nothing however you can extend or use it to rapidly develop classes of your own which perform required jobs for your program. An example could be a physics framework which could allow you to easily add physical simulations to your program (such as for CAD or a video game) which saves on the thousands of hours of work required to develop high quality physics.
2.) Is Microsoft Visual C++ what they call an "IDE"
Yes it is an "Interactive Development Environment". If you use Community edition you can add productivity plugins (recommended by professionals) to enhance it further. You cannot do this in express however as the Express licence does not allow that feature.
3.) When the game development questions come out, Qt is always mentioned. What is this QT thing? It has a QT framework whatever that is.
I will answer this with another quote.
Qt is a cross-platform application and UI framework for developers using C++ or QML, a CSS & JavaScript like language. Qt Creator is the supporting Qt IDE. Qt Cloud Services provides connected application backend features to Qt applications.
Qt, Qt Quick and the supporting tools are developed as an open source project governed by an inclusive meritocratic model. Qt can be used under open source (GPL v3 and LGPL v2.1) or commercial terms.
It is a graphics framework that abstracts and generalizes some graphical operations in a way which is portable.
If you are only targeting Microsoft platforms I would recommend sticking with the DriectX framework and possibly their various gamming frameworks if you want to easily port to the Xbox One.
4.) For other reference. Is Warcraft 3 world editor an IDE for the JASS programming language that Warcraft uses?
No as it is not interactive. The only feedback you get is when you save the map which can even crash the editor in response to some syntax errors.
IDEs generally offer you features such as automatic formatting of your code as you type, suggestions for what you might want to type (useful if your class has hundreds of members and you forget the exact names) and live syntax checking (syntax errors are shown up without having to compile first).
Eclipse is an example of an open source IDE used on Linux mostly (but not entirely) for JAVA development.