I would have to go with Churchill too. Sources seem to vary, but at approximately 700 KIA, Korea is to date the bloodiest post-WW2 conflict in which the UK armed Forces have been engaged. Although the war broke out before he was elected, the main British effort in the conflict occurred during his premiership. To that you have to add the casualties from the ongoing Malayan Emergency and the start of the Mau-Mau uprising in Kenya (although Army casualties in the latter were not numerous).
Unlikely, see my comment above ref- Churchill. Without going back to the books, I'd say that there were approx 350-400 regular UK military KIA during her terms of office. Just over 250 from the Falklands and the rest from NI related incidents. I have to admit that the latter is a conservative (no pun intended) estimate, and may be a little higher in reality.