A non-relativistic quantum state will return arbitrarily close to its initial state an infinite number of times. There is such a thing as interaction-free measurements: you can take photos of things without ever letting light hit a detector and you can tell whether a bomb is "active" without actually interacting with the detonator.
Energy is just a number that is calculated as a function of the state of a closed system — that this number is a constant results from the time transitional invariance of the laws of physics. Similarly, conservation of momentum is due to the spatial invariance of the laws of physics, and conservation of angular momentum is due to rotational invariance. Also, conservation of energy does not hold under general relativity.