The amount of life you gain from Bighorner Rancher’s last ability is determined when the ability resolves. If at that time the greatest toughness among creatures you control is 0 or less (probably because all of your other creatures were destroyed or otherwise left the battlefield in response), you won’t gain any life.

Bighorner Rancher’s second ability is a mana ability. It doesn’t use the stack and can’t be responded to. If the greatest power among creatures you control is somehow 0 or less, no mana is added.