Religion is excluded from our government anyways, with the exceptions of candidate platforms to get votes. Religion would still be up to the religious institutions like the Vatican.
Not necessarily. In order for it to work, all inconclusive theories involving the Origin of Life must be excluded.
For instance, if the theory of evolution was officiated by the government, then all religious groups would be furious.
And yes, of course religion would have to be separated, the opposite would have to be true to allow atheists/agnostics, etc., to live comfortably within this system.
What I'm trying to say is that any inconclusive origin theories cannot be stated as fact and serve as a code of how the government is structured because it would exclude a certain group. Denying all inconclusive theories would help to avoid this problem.