We have a very detailed timeline for the Japanese high command's activity in this time. Hasegawa's Racing the Enemy is the best source for this kind of thing. Here's a previous response I've given that goes over the details.

Short answer is, they didn't find out about the attack on Hiroshima, or its alleged atomic nature, until the morning of August 7th, because the bombing itself cut off communications with the city. The Japanese high command met and talked about it, and decided to send a team to find out if American broadcasts about it were actually true and not just propaganda before discussing it much further. (Various diary entries by members of said high command reflect differing views on it. Some dismissed it as nothing new. Some thought it was something important. The key thing is, interpreting it, especially on August 7th, wasn't some straightforward thing with a uniform reaction.) They got a report back from the scientists on the evening of August 8th confirming it was an atomic bomb and confirming the scope of destruction. That same day, though, the Soviet Union declared war on Japan, and later that same evening, the Soviet Union invaded Manchuria. The high command set up a cabinet meeting to discuss the latter events, which were very disturbing to them, on the morning of August 9th. While in that meeting they got the news about Nagasaki; it doesn't seem to have changed their positions at all (things were tilting towards offering a conditional surrender to the USA). Note that Japan did not consent to unconditional surrender until August 14th.

Which is to say: it is a very tight time schedule for high-level state decisions that require a large group to meet. Arguably too tight if you really wanted to avoid the use of a second bomb (which wasn't what anyone was trying to do, but it often gets framed as "we had to use the second bomb because they didn't react to the first"). The ultimate timetable for the two bombs was set by judgments about weather conditions made by the people dropping them (from the island of Tinian), not high-level strategy.

On your other question: The Japanese did not appear to have been anticipating a second bomb so quickly. (Neither did Truman for whatever that is worth.) A nearby Army unit was dispatched to Hiroshima shortly after the attack to help with the aid to victims and to aid in burial detail. I don't know what you're asking re: other countries — it was World War II, and Japan was basically the last part of the Axis still around, so yeah, lots of countries, e.g. the Allies, were asking them to surrender. Japanese citizens did not call for surrender in any great way — that was not how being part of the Japanese polity worked at the time (those who were against the war were essentially persecuted, it was not a democracy, press was controlled by the state, and most were in favor of the war for nationalistic reasons).

I think it is important to remember that these bombings came in a context in which Japanese cities were being destroyed from the air (with conventional and firebombs) on at least a weekly (sometimes daily) basis, and in which there were large discussions about the role of the Soviet Union entering into the Pacific war. The atomic bombs were part of that context and discussion, but it is not like the Japanese high command were just sitting around and the atomic bombs were the only disturbing things that were going on from their point of view. It was a much messier and busier environment. Hasegawa, again, paints this picture very well.