Yes, you are correct on both :D Count Dooku was tasked by his superior to find a template for the army, and also received the order to eliminate some target who's name I forgot. So, he kills two birds with one stone by offering a bounty on said target, as a contest; Jango wins against another mandalorian and is offered the money and the chance to be cloned for the army; and he accepts on the condition that they give him the first clone, unaltered, to keep, who we all came to know and love as Boba Fett And yes; the 501st is the legion that was nicknamed Vader's Fist after they became the Imperial Army.