My choices from the limited selection available would have been(if I had voted):
Leaders: Winston Churchill
Explorers: Ernest Shackleton
Scientists: Albert Einstein
Entertainers: Charlie Chaplin
Activists: Mohandas Gandhi
Sports: Muhammad Ali
Artists and Writers: Pablo Picasso
Leaders: Nelson Mandela (and a worthy winner IMO)
Explorers: Ernest Shackleton (out of the selection - but Roald Amundsen is more worthy in a directly comparable manner to Shackleton)
Scientists: Albert Einstein (agree)
Entertainers: Rubbish selection and rubbish category focussing more on fame than influence as a musician/actor - so would choose any of them
Activists: Toss up between Gandhi or Luther-King - both worthy winners
Sports: Section is more based on non sporting achievements (effectively another 'activist' category) - so none really rock my boat. If pushed would go for Pele as a genuinely sporting great. In terms of someone who completely dominated their sport - with achievements never likely to be matched, then perhaps Bradman
Artists and Writers: Pablo Picasso - worthy winner