For those reading later: Yes, to both questions. EV gains are not applied all at once, they depend on the Pokémon’s level. We say that at level 100, every 4 EVs give 1 stat point, while at level 50, it takes 8 EVs for the same effect. EVs accumulate and are stored, and their effects are applied gradually as the Pokémon levels up. According to the stat formula, just like Natures only give or take 10% at level 100, the total gain from 510 EVs (127 points, or up to 63 in a single stat) is only fully seen at level 100. Before that, you only get a fraction of the full benefit. And finally, a Pokémon's stat is updated with each level up( And other things too).