Ad 1
No idea, that is wonky AI I guess.
Ad 2
What is wrong with that? Maybe she thought she could take you on and she tried it. Europeans in the age of colonization needed little reason other than 'Oooh, shinies!' or 'look, we can push these natives around!' to start wars and claim land. Why would you expect the AI to act any different?
After that, she took peace but she was clearly utterly disappointed and not content with how the war went. She publicly announced that you are not to be trusted. Is this really out of the way of how you expect some spoiled rules to act? If this was a board game, I can totally understand her move. In fact, that is how me and my friends play the civ board game. We denouce at will.
Ad 3
the AI clearly has no idea if you play one city challenge or not, apparently the AI considers all games as equal. In that game - that as far as the AI knows is a normal game - the AI would prefer it if you would not settle next to it. It matters little who settled next to whom, what matters in the eyes of the Ai is that you do not do to it what it just did to you. Again, is this so far fetched? Again, in the civ board game, we do this all the time.
Ad 4
How is this not understandable? There is a recent real life example of a certain ruler of a country in north Africa who reacted just the same. In the 20th century, there are several exemples of nations doing just that in a war. Why would you expect the AI to react differently?
Sometimes people do not take the time to consider all alternative outcomes and pick the best one. Sometimes people act emotionally, and blurt out the first thing that comes to mind. This can very well be a primal reaction, rather than a higher cognitive one. The AI does just that. Goodjob methinks!
Edit: Yesterday I played a game where Cathy was at war with me, and she pretty much begged me not to wipe her out. Of course I still did it. So basically what you can see from the AI is any range of behaviors, from 'please do not kill me' to 'I will never surrender'. Pretty impressive, huh?
Ad 5
After the Ai wipes out a nation, most players think 'hmmm, I will have to do something about that AI somewhere in this game.' When you wipe out a nation, other nations consider you a war target. Why is this odd?
I don't know why the other leaders denounced you. There are any number of things that can trigger that. On this info, we cannot be certain. I know that AI leaders have a tendency to have moodswings, and that relations can shift quickly. This is pretty much like in real life. Also, this is like a board game would be played.