/u/jslsj

You are asking a set of complicated questions, and some of them are really best answered in the context of political theory (meaning, not on this sub). Please consider compartmentalizing the questions.

The idea of control of the seas as we know it today is quite new. It was only promulgated in 1982 through the UNCLOS (United Nations Conventions on the Law of the Sea). The prevailing idea of any control of the sea -- the so-called Law of the Sea -- is usually attributed to Cornelis van Bijnkershoek, a Jurist who developed the idea of sovereignty over adjoining waters based on its ability to enforce control over it. Thus, the idea that "a state owns the adjoining sea up to a cannon-shot's distance away from its shores." This defines the national maritime boundaries. Beyond that, all seas are free to all nations and belongs to none of them, the concept of Mare Liberum by Hugo de Groot.

That idea lasted until the post-WW2 era, when nations started to desire resources beyond their shores, namely minerals, fisheries, and control over aspects of shipping in particular over pollution. One of the significant changes were made by US President Harry S. Truman, who promulgated Proclamation 2667 in September 1945 stating thus:

Whereas the Government of the United States of America, aware of the long range world-wide need for new sources of petroleum and other minerals, holds the view that efforts to discover and make available new supplies of these resources should be encouraged; and

Whereas its competent experts are of the opinion that such resources underlie many parts of the continental shelf off the coasts of the United States of America, and that with modern technological progress their utilization is already practicable or will become so at an early date; and

Whereas recognized jurisdiction over these resources is required in the interest of their conservation and prudent utilization when and as development is undertaken; and

Whereas it is the view of the Government of the United States that the exercise of jurisdiction over the natural resources of the subsoil and sea bed of the continental shelf by the contiguous nation is reasonable and just, since the effectiveness of measures to utilize or conserve these resources would be contingent upon cooperation and protection from the shore, since the continental shelf may be regarded as an extension of the land-mass of the coastal nation and thus naturally appurtenant to it, since these resources frequently form a seaward extension of a pool or deposit lying with the territory, and since self-protection compels the coastal nation to keep close watch over activities off its shores which are of the nature necessary for utilization of these resources;

Now, Therefore, I, Harry S. Truman, President of the United States of America, do hereby proclaim the following policy of the United States of America with respect to the natural resources of the subsoil and sea bed of the continental shelf.

The above was driven in part by the desire of the US to develop subsurface oil deposits that lie under the Gulf of Mexico.

Of course, other nations followed suit and thus began a series of disagreements on maritime boundaries. The UNCLOS is an attempt to make sense out of all these claims. The Exclusive Economic Zone that is 200 nautical miles from the coastline (EEZ) is one aspect of the UNCLOS definitions.

If you pay attention to geography and geology, you should realize that the US's claim on the continental shelf off its territory is more vast than the EEZ. Thus, the US accepts UNCLOS except for Part XI, which governs this.

Regardless, all claims are based on coastlines, which makes islands and islets key. You can only claim a part of the sea that is within some distance or metric from a land territory upon which you have sovereignty. Thus, the PRC's claims upon the South China Sea is based upon sovereignty over islands in that region.

I will not comment on contemporary claims of sovereignty, but I hope the above gives good context.

Want to know more? S.N. Nandan's The Exclusive Economic Zone: a Historical Perspective is available online and is a great read.