The last ability can target any creature, not just a tapped creature (it doesn't say "target tapped creature"). When the ability resolves, check whether the creature is tapped or not. If it's tapped, you may destroy it. If it's not tapped, the ability does nothing.

The abilities are separate and cumulative. If another creature you control is both of the listed colors, it will get a total of +2/+2.

If you cast a spell that's both white and black, the last two abilities will both trigger. You may use them together to destroy any creature. To do so, put the "destroy" ability on the stack first, then put the "tap" ability on the stack, with each one targeting the same creature. When the abilities resolve, they'll tap the creature, then destroy it.