Opponents who have left the game aren't counted by Blazing Sunsteel's first ability.

Blazing Sunsteel is the source of the middle triggered ability, but the equipped creature is the source of the damage. For example, if the equipped creature is green, that ability can't target a permanent with protection from red, but it can target one with protection from green, though the damage would be prevented.

If your life total is brought to 0 or less at the same time that the equipped creature is dealt damage, you lose the game before Blazing Sunsteel's middle ability goes on the stack.

A creature can be dealt an amount of damage greater than its toughness. For example, if the equipped creature has 1 toughness and is dealt 3 damage, it deals 3 damage, not 1, to the chosen target.