You're asking a couple of different questions here, but on the question of your life insurance; if you die; it will pay out.
If you've had the life insurance for over a year and commit suicide; it should still pay out. Less than a year, then your company will be looking for evidence of you having phsycological problems. IE, have you been to see your doctor to tell him you're suicidal. If you have, it should still pay out.
So with accidentally falling off a ladder and dying; you should have no problem, since you never did it on purpose like the other scenarios.