Relationship Between Ratio of Atmospheric Gases and Ocean Gases
The law that governs the pressure of gas at equilibrium over a dissolved liquid is called Henry's Law. Note, the equilibrium assumption, as there is some time dependence. That is, if you start with no dissolved gas in pure water, then in a relatively short amount of time, the amount of dissolved gas will be less than equilibrium.
Let's talk in abstractions. Henry's law's temperature dependence resembles the Clausius-Clapeyeron equation, so we can draw some parallels. From the Wikipedia link, for a given gas, the Henry's law constant is $$H(T)=H(T_0)\exp\left[-\frac{\Delta K}{R}\left(T^{-1}-T_0^{-1}\right)\right]$$ .$-\frac{\Delta K}{R}$ is Wikipedia's version of $-\frac{\Delta_{sol} H}{R}$, but I used $K$ to not cause confusion. For pure water, this link shows the solubility of different gases at different temperatures, but most relevant is the temperature at 0$^\circ$C (that is, it gives $H(T_0)$).
But all of this doesn't answer the two questions that your question boils down to.

Raising the temperature decreases the solubility of a gas.
If the pressure increases, then the amount of gas that can be dissolved increases per Dalton's Law. If the system is not in equilibrium, then the amount of solute will increase in proportion to Henry's Law.