Newton's first law states that every action must have an equal and opposite reaction. So how does splitting a tiny atom with a few electrons create a massive burst of energy?
As small as those little guys are there are some very strong forces holding them together. Breaking those bonds is going to release that energy.
Also, if we all came from the same place, and we all started off as a bunch of stuff even smaller than atoms, how do we join? How do we become electrons, and get energy, how do they join and become atoms?
I am not a physicist so I can not answer these. I could attempt to contact my brother for the answers because he is a physicist.
How does an atom of one element become all the elements of the periodic table?
Stars do the job. They are huge pressure machines because of the large amount of gravity and they break apart atoms which allow for the formation of newer, larger elements. Our sun turns hydrogens into helium and it is a fairly small star compared to others. An interesting side note, helium was first discovered by a spectrum analysis of the sun.
How do those elements then start joining back together to form compounds?
Atoms interact with each other through the electromagnetism, strong interaction, weak interaction forces. They can bind together in many ways such as sharing or donating electrons from one to another. All of this is easy to look up and even test yourself.
And the kicker, how do random compounds made by chance, somehow make little living, active things? (bacteria).
Most people, especially scientists in the field, are not going to claim that these compounds came together by random chance and formed life. It is known that the necessary aminoacids and nucleotides that life uses do form in certain conditions, and these conditions were much more common on the early earth. These aren't randomly forming. There are a series of processes that bring these together and they all follow physical rules which is why creating them in a lab is repeatable. It has also been discovered that self-replicating compounds can form in these environment. They usually form when an area is being constantly flooded, dried up, and flooded again. I do not know why they form under these conditions chemically as I am not a chemist, but I have read peer reviewed scientific papers about them which adds to the credibility of this concept for me. After that it is still a long process to getting to an early thing we would call life. However once you have self replicating systems in environments that are full of the stuff it needs to replicate you get processes occurring that are similar to evolution. This occurs because the replicating compounds do sometimes make errors which sometimes cause them to be less stable but other times more stable for the environment. Eventually you get to systems of these molecules that work together as a sort of colony similar to the colonial bacterial or colonial protists but with each unit being much more simple. After several other processes these would come together to become what most scientists would consider to be life.
Remember that bacteria are giants in complexity and that scientists are not saying that the first self-replicating compounds that led to life were anything near the complexity of modern bacteria.
How do bacteria somehow join and mutate to become organisms that are then harmed by those same bacteria they came from?
Well they are probably just being harmed by bacteria that are more basal to its common ancestor. Bacteria are always competing with each other for resources and some evolve ways of harming other bacteria to take their resources from them, even kill them to do so. If you are talking about how life eventually became multicellular than you need to understand a lot of complex concepts, such as endosymbiotic relationships, that allowed for prokaryotes to become eukaryote.
How do those organisms become totally different, totally separate organisms that have completely different traits and why?
Mistakes in replicating the genetic information, genetic material from other sources being mixed into it by horizontal gene transfer, and even new information being placed in by viruses. These are all sources for change. Sometimes they are harmful and sometimes they aren't. Sometimes the changes are slightly harmful but not harmful enough to kill off the organism. The organism and its descendants survive and eventually changes that will change the somewhat harmful change into something useful. I have digressed, back to the main point, these changes can occur and they will be passed on if useful, neutral or not harmful enough to kill off the line. These changes can accumulate and be selected for or against under different circumstances.
If our only purpose is survival, why didn't those bacteria (most likely cannibalistic, else how did they survive?) just stay as bacteria. And if survival's the game, why would they mutate into things that can be killed by the same bacteria they came from?
There is no guiding force. The bacteria don't know where their changes are going to take them. The bacteria don't think about how they are going to change. If there is a niche to be filled and a change arises to fill that niche than those individuals will have an advantage to survive. The selection process doesn't just produce the best of the best, it produces replicating structures that are able to survive in the environment. If it is able to survive than it will. There are reasons for more complex organisms to be more successful in certain environments.
I think you have a misunderstanding of evolution due to you saying "why would they mutate into things that can be killed by the same bacteria they came from?". I don't know when this supposedly occurs. Sure some of the organisms might have more basal characteristics to the common ancestor but that doesn't make them the exact same organism.