Equanimity, aversion and anatta Equanimity is described as It refers to the equanimity that arises from the power of observation, the ability to see without being caught by what we see. The definition can be found here. 

If i dig further at look at the concepts as set by Buddha at http://www.insightmeditationcenter.org/books-articles/dhamma-lists/, it confuses and muddles my understanding.

If i attempt to understand not rationalize the description of equanimity, i gather that if an emotion arises or is arising, i observe it. This emotion may be happiness, love, sadness, hatred, dislike, etc. As long as i don't interact or engage the emotion, i am mindful and aware. 

Again because i tend to look to examples be it in nature or behavior, i will attempt to describe my understanding. 

Example 1

Surrounded by children, in laughter, there is a sense of happiness and innocence. If i simply observe the emotion of happiness, should i not participate in it? Yes, it may be temporary but isn't that being in the present or moment all about?

If i am devoid of emotion and only an observer, am i not practising aversion?

How does this differ to physical interactions?

Example 2

Relationships are strained between 2 or more people. The fact that they have stayed away from one another reduces the strain as it does the thoughts that arise from remembering incidents. Over time, people sympathize as well as empathize. This leads to the belief that should they meet again, they will have better understanding.

Is staying away deliberately considered aversion? If someone had been
abused and they stayed away from their abuser, is it aversion?

Is not wanting to think about it aversion?

Is the 'loss' of memory and an understanding on the path of anatta?

Does this 'loss' of memory and thought as well as an understanding of the situation and experience lead to the path of equanimity?
I'll try to answer as broadly as possible and I hope it becomes a little more clear. But if you want more detail or deepening in one or more of you questions, I suggest you to post new specific ones.


  As long as i don't interact or engage the emotion, i am mindful and aware.


For me it seems the order is quite opposite. As long as I am mindful and aware, I don't get too involved with phenomena, and then no strong emotions takes over. If I don't get caught by what I see, what I perceive, my mood don't oscillate, my temper is even, there is equanimity.


  If i simply observe the emotion of happiness, should i not participate in it?


You don't need to choose to participate or not. When they happen you only observe them.

So I think the question is not whether you should or not participate in emotions. But how is you attitude towards what you perceive and how and why these feelings emerge. When it is told to observe, it is not to perceive just the emotion happening. But it is to see the whole process, from its origin and development to its end.


  If i am devoid of emotion and only an observer, am i not practising aversion?


It could be aversion, it could be disregard. If you can't feel, or you ignore your all feelings, how could you be compassionate? Equanimity isn't to be devoid of emotion, but to not have strong mood oscillations.


  Is staying away deliberately considered aversion? If someone had been abused and they stayed away from their abuser, is it aversion?


Maybe yes, maybe no. It depends on how you feel about meeting the other person. You could feel disgusted by just thinking about someone and totally refuse to meet that person. You could feel sad about that person and prefer to not meet him/her.


  Is not wanting to think about it aversion?


It really depends on the attitude towards the thought. Refusing it and fighting against it forcefully is one thing. Now, observing it while letting it be and letting it go is another thing.


  Is the 'loss' of memory and an understanding on the path of anatta?


If I understood your question correctly, no. Anatta is about perceiving the ultimate reality, there is a QA about it: What is the precise meaning of anatta? It isn't about "losing" memories, but more about not clinging to them and not getting overwhelmed by them. Anatta is perceiving that apparently there is a self with memories, thoughts, feelings, and so on, but none of these even the self are permanent or absolute. And it isn't much about intellectual understanding, but about perceiving, observing.


  Does this 'loss' of memory and thought as well as an understanding of the situation and experience lead to the path of equanimity?


Quoting the text you referred, "through the power of observation equanimity arises". Through observation you can stop feeding bad memories and undesirable thoughts, eventually if you stop feeding it, it won't be able to bear fruits.

Understanding the situation and experience is somewhat a dilemma. It could make you feel more comfortable, it would yield clearer understandings, but you are still feeding the memory anyways.

Equanimity happens when we don't cling on phenomena, when we relax our attitude towards phenomena - again - through the power of observation. When an emotion happens you observe it, let it be and don't get caught, don't get overwhelmed by it, don't let it take over. Stay calm and let it go away by itself.

Sheesh, I think you still got questions, so I suggest you to post specific ones, if you will. Try to find some key doubts that will help you lead your reasoning.