This question reminds me of questions like "How to learn organic chemistry" or "Why is it so hard"? The difference in whether these are hard questions or easy questions depends on what training one has had or how they go about trying to solve them.
I have posted an example of the Claisen rearrangement
here. I think this should enable one to answer several (but not all) of the questions posted. Obviously, I favor a mechanistic approach to solving these questions. Since the questions themselves introduced the reactions, it essentially was asking for a mechanistic explanation. Therefore, I am guessing the poster may not have been familiar with these mechanisms.