Was the Manhattan Project immediately declassified after the first bomb was dropped in Japan? What was the communication about the program like after the weaponry has been used?

There was an elaborate and multi-pronged "Publicity" campaign to release information about the Manhattan Project and the atomic bomb directly after the Hiroshima bombing (which some called "Publicity Day").

This included:

Press releases by President Truman (written by Arthur Page, the VP for Marketing at AT&T) and the Secretary of War, Henry Stimson (written probably by his assistant Harvey Bundy). Truman's press release was the first real announcement, and was released 16 hours after the Hiroshima attack (prior to this, it was all still secret). Stimson's was longer and more detailed, and described the history of the Manhattan Project and some of the technical achievements. There were also statements released by the British and Canadian governments.
Newspaper stories that had been written by William L. Laurence of the New York Times, who was on the government payroll (and, as it turns out, the NYT payroll as well). These were written by Laurence and then edited for security and prose-style by US Army lawyers. They also set up a Manhattan Project Public Relations Office at Oak Ridge, that could coordinate queries and responses from journalists.
Three days after Nagasaki, Truman approved the release of a history of the building of the atomic bomb called "A General Account of the Development of Methods of Using Atomic Energy for Military Purposes," written by Henry DeWolf Smyth, chair of the Princeton Physics Department. Smyth had been commissioned to write this during the project itself, and its goal was both to give as decent a technical overview as they felt was safe to give at that time, both for the purposes of encouraging democratic (and global) understanding of the nature of nuclear weapons, but also to serve as sort of a guide to project participants about what they could talk about (if it was in the book, they could; if it wasn't, they couldn't).

They didn't issue any kind of formal declassification order because those didn't really exist yet. The entire "declassification system" as we think of it today evolved in the months after the atomic bombs were dropped, and General Groves and others realized that the above releases were not sufficient and they needed a real system. This system was created by a Committee on Declassification, chaired by the physicist Richard Tolman, and developed the system of document-based declassification with Responsible Reviewers and declassification guides and the like.

So in short, there was quite a lot of thought and effort and preparation put into what was going to be released about the bomb, and how they were going to use those releases to paradoxically make it clear to people working on the project (and journalists, as much as they could be controlled) what the limits of discussion were. It is interesting, and not as contradictory as it seems, that they could use publicity in the service of secrecy. They were very selective about what they released, but it looked like they released quite a lot — this was deliberate, and was meant to keep journalists from digging too deeply, and to keep project participants from feeling tempted to tell stories the military thought they ought not.

Perhaps annoyingly the best source on all of the above is my book on the history of nuclear secrecy in the United States, esp. chapter 3.