In Marineford, there were other people than Luffy who had Conqueror's Haki (Whitebeard, Hancock, etc.). Why didn't they use it when Ace was about to get beheaded? Because if Luffy did not use it unknowingly, Ace would have died sooner. Or was it the case that no one had Conqueror's Haki as powerful as Luffy's which could act at a large distance?
Yes, there are other people who could use Conqueror's Haki at that moment. On rescue team, they're Shirohige and Hancock. But only Shirohige knows about Ace's situation and Hancock was fighting somewhere else. However, Shirohige wasn't in good condition to use Conqueror's Haki. He was sick and badly injured by some attack by Marine just before Ace's execution order.
Some other source said Conqueror's Haki needs heart to use it and Shirohige couldn't use Conqueror's Haki because his heart was injured. But at this point, I can't find any canon source to endorse the statement.
whitebeard not use Conqueror's Haki because it effect on all peoples without powerful will so his man also effected with that. It's king personality i think
It's simple, you need extensive training to use Conqueror's Haki. Only certain people like Luffy, Rayleigh, Shanks, and Doffy trained their Conqueror's Haki.