Currently the only set of programs that can do all of that under one roof is the Adobe Creative Suite, which is quite expensive and uses a suite of different editing packages that can be integrated to produce a final result.
The problem is with your first requirement. There is a lot of difference in the types of animations. From stick drawings you could do in paint and save as jpegs and import as frames into any editing package to produce moving images or a full blown animation package to do full 3D rasterized,ray traced epics that would require serious processing power.
The latter could be done with a free program called Blender. and the results saved as movie clips.
Then something like Movie Edit pro could do the rest whichever way you choose to produce animations.