I'm kind of confused as to what exactly all of those mean and do.

I know Law cuts down corruption and increases public order. But I'm not sure what happiness does, does it only increasue public order without actually doing anything else? If that is the case why even refer to it as happiness when there are several buildings that only increase "public order" without mentioning "happiness"?

While on the topic, I know at 65% and below there are riots and increasing chances of revolts. After the 70% level does having a higher public order have any other direct effect other than creating a buffer in case units or governors are removed?