Here we would call that Aizen a "Mariposon"... which roughly translates as Butterfly-boy. Though we use it the context of 'gay'
Not the Hogyoku. Aizen was paying those random Shinigami for 'something'. And that 'something' involved beating up a young Rangiku. Thus Gin's purpose became to get close to Aizen and kill him because he caused that beating. Talk about patience... that must have happened centuries ago.