- Yes, Blender has a node based compositor that works with video. Sound files and straight video cutting can be done in Blenders "Video Sequence Editor".
- Blender can do 2D animation, but not necessarily like flash. You could make something that looks 2D (exactly like that chart) but you have to make it in Blenders 3D working environment. Unless you rig the whole thing up in the compositor.
- The node compositor is available to use for image editing. Texture painting is available for texture creation as well as procedural textures. You will not find as many creation tools you would find in Photoshop.
- As far as I know you can't use Blender as an audio recording program, but you can edit audio together in Blender. So maybe use Audacity to record your audio and use Blenders "Video Sequence Editor" to cut the audio with your animation.
5 - 10 minutes of animation is a lot a lot of work. It's one thing to know if Blender can do something, another to know how to do it, and another to actually be able to do it, and another to be able to do it well in a timely manner. :) If you plan to do everything you listed above, you have your work cut out for you. Best of luck!
To dive down the rabbit hole with all this stuff. Mine the great Blender Cookie :)
http://cgcookie.com/blender/category/getting-started/