Regarding the second point there, nature always tends toward equilibirum. The only way water would achieve a level greater than 100% saturation is if conditions change -- such as the water warms up quickly. Given constant conditions, nature won't overshoot equilbirum and then have to come back down. Outgassing would only occur if conditions significantly changed from a previous state.
Super saturation of oxygen in water does happen in nature at certain times and conditions. There is another source of oxygen in water, besides diffusion law and water movement, and this is called photosynthesis.
Then you would think wrong. Because the laws of diffusion do not change depending on the medium it is diffusing through. Diffusion through a gas, liquid, or a solid are identical. Now, the specific diffusion rates will be different, but the laws remain identical, and hence the mathematical forms of the solution remain identical.
Do you really claim that diffusion of gas in water and diffusion of gas in air happens at the same rate?
When you use a mathematical formula that contains non-constant values which change depending on the conditions, such as these in a diffusion law, the solution is hardly identical.