based of the race on the mountain hill, hayate seems to have no problem racing aggressively so its entirely possible he ran someone off the road in the past and they crashed/died
the daigo in this series (toake daigo) is completely unrelated to the original daigo (daigo asahina). their name connection gets explained later. current daigo has had a bad shoulder since childhood
the text was confusing as a lot of it was gender neutral terms (+ otaki is a gender neutral name), but i figured since they were twins, it was more likely they were brothers but im still not entirely sure