At level 36 or 37 I believe. Well, it's before level 40 I know that, much earlier than Swampert. And the Mudkip line get BETTER after beating Norman because you can get Ice Beam on the sunken ship and Ice is strong to a lot of common types. You can beat the whole game using only Mudkip and its evo's. I've done it.
And yes, all but 5 natures effect stats. Hardy, Serious, Docile, Bashful, and some other one are nuetral natures, others will increase a stat while decreasing another, like Adamant which increases Attack but decreases Special Attack.