Someone well-educated in the matter, please tell me what the Big Bang and Evolution theories actually are?

The big bang is a misnomer. Current theory suggests that a singularity formed - no one knows why - and then expanded into the current universe - which is still expanding. Because E=mc2, there is no need for matter in the primordial singularity, only energy. As that energy expanded, it became matter as it cooled. Someone else can explain things about evolution.