(Disclaimer: All the following based off of Watiggi's thread)
1) Founding a Corporate HQ requires a specific GP.
2) If you found a Corporate HQ, then you get 1 gold per city with that Corporation.
3) "Competes with..." means that only one corporation per resource requirement can be in any one city at any time. Additionally, if you want to kick out a competing corporation, it costs you much more than founding a corporation would typically cost you.
4) Spreading a corporation to another city requires building a corporate exec plus some gold, and requires that your empire can satisfy the resource requirement of the Corporation, within the city where the corporation is to be spread.
5) Spreading a corporation into a foreign city costs more than spreading a corporation into your own empire's city.
6) "Resources consumed..." Means that the city that you want to have a corporation in must meet the resource requirement, i.e. your empire has access to this resource, and the city, via trade routes, also has access to said resource.
7) Benefits stack if multiple non-competing corporations are in a city, and they are multiplied by the number of times that said city can satisfy the resource requirement. For example, you have 3 coal that your city has access to. You spread Aluminum Inc. into this city. Now, you get 3 sources of Aluminum, and you also get 3*3 = 9 beakers in the city.
I don't believe corporations can spread via any means other than a corporate executive, which is built in a city that has the corporation which you want to spread.
Corporations also have a maintenance requirement, which the host empire must pay.