How does morality relate to God?  Is the acknowledgement of God even necessary for practicing morality?

Whether life was created by God or was the result of an accident that converted "nothing" into material existence has no bearing on morality.  Morality is necessary for life, in either case.  Morality is those actions and behaviors allowing life to sustain itself as long as it can and as well as it can.  We practice morality because we want healthy and happy lives, not because some superior agent is telling us what to do.

If the living world is an accident, then we still want health and happiness in order to sustain this unique experience.  

Religions existed long before modern medicine and science.  Before the sciences were developed, people had to rely on common sense and direct experience.  Our ancient ancestors spent more time listening to nature and hearing its subtle messages.  Today, we have new insights born of science, which help us to better understand those actions and behaviors that lead us to maintain good health and happiness.  

Ironically, modern technology has also made us quite deaf to nature's message with all its distractions.  A disproportionate amount of our time is spent on activities that do not support our life, and many activities that actually shorten it.  

Regardless, morality has only one purpose and relies on only one principle.  Morality is those actions and behaviors that lead to the good health and well-being of individuals and communities. Practice behaviors that lead to good health and happiness for ourselves and others, and we will be moral citizens.