For your main question — news of the success of the Trinity test was initially known to the United States, quickly conveyed to the British (partners in the project), and was indirectly indicated to the Soviet Union (Truman told Stalin that they had a new weapon they were going to use; Stalin already knew about the existence of the project through espionage and that a test was planned, and from this he inferred correctly that the test was successful). These latter events took place during the Potsdam Conference in Germany, in late July 1945. The Canadians had a role in the project but I am not sure they were told about the Trinity test — I doubt it (their role was not as direct as the British). No other Allies (e.g. the Chinese) were told about the test. The goal, of course, was to maintain absolute secrecy as much as possible, so that the Hiroshima attack would come as a great surprise and shock to the Japanese.

(On the US, UK, and Soviet initial reactions to the success of Trinity, Michael Gordin's Red Cloud at Dawn discusses this in the early parts of the book.)

No other countries were told about the Trinity test and I've never seen anything to indicate they were aware of it directly or indirectly. Of course everyone learned of its existence after Hiroshima, because it was revealed as part of the post-Hiroshima publicity about the atomic bombs.

As for your second question — I have no idea, but the numbers of neutral countries is quite small: Ireland, Portugal, Switzerland, Spain, Sweden, and their colonies and a collection of very small states. I have not seen any work on, say, the Spanish response to the atomic bomb, or the Irish response.