It's both a law and a rule. This usually refers to something that is a physical law, but also can simply be a law, too. Anyways, lots of rules. Lots of laws. It's both, so the stronger one (law) takes precedence.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.
That bacon was eaten by Mami according to the law of nature.
The teacher was puzzling over how to teach the law of gravity.
If a rabbit jumps straight up in the cabin of a high speed train, according to the law of inertia, it will land in the same place.