It is just as safe to carry on the half cock notch as cocked and locked, and certainly safer than hammer down on a loaded chamber.
Absolutely not. A blow to the hammer will not impart any energy or motion to the firing pin if the hammer is down, but if the hammer is partially cocked -placing the hammer in position to be struck a blow, unlike full cock - a blow strong enough to shear the half-cock notch might very well transfer enough energy to the firing pin to fire the gun.
The gun is not as safe when at half-cock, and in fact, you effectively deactivate a couple of built-in safeties by doing so. See, that's why I said "everyone" knows.