Is activation energy related to reactivity?
If by reactivity you mean, "does the reaction occur quickly", then yes, a highly reactive molecules do have a low activation barrier. The fastest molecules can react bimolecularly is if they do so on first encounter with one another. This effectively means that  there is a very small potential barrier between reactants and products so that they have enough energy, at the prevailing temperature, to always overcome this. In solution the rate constant is determined by how fast the molecules can diffuse together and in mobile solvents such as water or acetone the bimolecular rate constant is around $\ce{10^{10} dm^3mol^{-1}s^{-1}}$ depending on exact solution viscosity and far less in viscous solvents such as glycerol.

If by reactivity you mean that the reaction is very exothermic, i.e. free energy is large and negative, $\Delta G &lt; 0$ then there is generally no way to precisely predict how big the activation barrier will be. It is usually measure using the Arrhenius equation and plotting log(rate constant) vs. reciprocal temperature. I'm not sure if ab initio quantum calculations can predict this in general. In fact many exothermic, thermodynamically spontaneous reactions occur slowly. Most organic substances react with oxygen exothermically, but are quite stable, because the activation energy to do so is so large. You and me for example :)