I just want to ask which software is best or which software is mostly used on these 2D animations.
I know that Flash is commonly used, but I just don't like Flash much, so I am looking for alternatives.
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Any number of tools could be used, and best is not defined since it depends on what you know how to use. The second example quite clearly says it was done with Processing. You could choose amongst any number of tools at your disposal. Possible tools to use are (this list is not exhaustive by no means):
Don't discount possible 3D animation tools, all 3D can do 2D. For example the animation in image 1 (below) was actually made with Maya. Just converted to a gif in Photoshop. All of the effects you list are trivial to do in Maya, if you know how to use it (Mayas learning curves is pretty steep though).
Image 1: Animation made for teaching and used here, made with Maya. Arbitrary demo easily at hand.
Nearly any animation tool can be used.
I can't say if it will do what your examples rendered, but you could download the trial version of Toonboom and give it a try.
Different versions are on that page, one of which might fit.
I work personally with synfig to make 2D animations. I've chosen this one over other paid ones because it is Open Source and has an easy learning curve. Here is the web page: http://www.synfig.org/cms/
Here are some animations I've made using synfig: http://www.dreamstime.com/videos-and-animations-colldet22095#res4185687
If you look at the pages for each of those examples, you will find clues and/or explanations of the software for the first two.
The third isn't specific, though I'd put money on After Effects there as well.
To achieve the look from your examples, a vector based animation software could make it easier and I`ll recommend AnimeStudio. There are many other programs but it mostly depends of your skills in animating, workflow or sometimes it could be just the interface.
To be more specific, if you have an idea how to create and achieve transformations like in that example with cameras, you could easily make it even with MS Paint and MovieMaker. Creating frame by frame, picture by picture and eventually you will end up with the video, but I would still recommend vector based program just to avoid the FbF approach (could be tedious and it`s never about the tool but the one handling the tool ,)