*gasp* I missed this one. Actually I forgot it
The Trade and Commerce Boxes work the same way the Shipping Boxes work in CW2, except the Trade Boxes (Circles) are limited in their influence to their respective areas, noted in the tool-tips of each Trade Box. So they allow for moving supplies as well a generating income.
The tool-tips also state that you require an "overall marine superiority". I'm not sure, but probably only combat elements in the Trade Boxes are counted, and how binary the calculation is, I don't know. If it works like in CW2, enemy combat ships reduce income. The more enemy ships, the greater the reduction.
I'm not sure if there's any advantage of Commerce Box over Trade Boxes. Maybe just a question of putting all your eggs in one basket. ROE probably does play a role though too.
Blockade Box probably works pretty much the same as in CW2. Using it is a question of strategy, so no simple answers.
Brown Water Blockading works the same as in CW2 AFAIK. You'd have to look at what is in a city to see what impact it might have. Also check for multiple exit-points.