1. Which language is more widely used?
In general I'm not certain, outside of legacy applications and projects with unusual performance requirements C++ isn't used much in most business applications anymore; but C# is far from ubiquitous, and there is a lot of competition from various other programming languages, and even those who focus on the .Net platform may choose other languages to develop with.
2. Which is easier to learn and use?
C# by far, but that isn't saying much ...
C# is a newer, higher level language with far more libraries, documentation and frameworks which gives you a lot for "free". With that said, C# is still a very clumsy language with some semantics and syntax which make it less than ideal to learn to program with.
3. Which is better to learn for game development?
If you want to be a high end game engine developer you would want to know C++ ...
For a novice programmer who wanted to develop games I would suggest you learn the scripting language that is associated with a very simple game engine.
For a more experienced programmer who wanted to develop some simple games on their own, I would recommend C# because Microsoft has created some nice abstractions and integrations between the .Net framework and DirectX to make game development easier.
4. Which is better to learn for software, programs and app development?
Any language will do, but C# (more or less) limits you to development for windows platforms ...
5. What's the major difference between them, anyway?
C++ is a low level pre-compiled procedural programming language with some object oriented programming concepts built into it ...
C# is a mid-level interpreted object oriented programming language ...
In general, I would recommend neither for a beginner though ...
Scratch is probably a good place to start because it was specifically designed to make programming more accessable ( http://scratch.mit.edu/ )
Many people I know rave about smalltalk, and Squeak is the open source implementation of smalltalk ( http://www.squeak.org/ )
Beyond those, Python and Ruby are also good options.
