Practically all physicists knew that atomic bombs were theoretically possible after the discovery of nuclear fission and the nuclear chain reaction in the early months of 1939. Most thought that they were a technology that was not going to emerge for another decade or so, and if they were interested in chain reactions, they focused on the possibility of using them to generate power, which is a much easier problem than that of a bomb. The idea of atomic bombs had been "in the air" in a general, science-fiction sense since 1914, but certainly by 1939 they were a common trope in "gee whiz" newspaper and magazine stories. When fission was discovered there was plenty of press about its possibilities, though, again, scientists had long grown skeptical about the idea of being able to release atomic energy on an industrial or military scale, because most of the discussion of it had been uninformed nonsense, and there were many technical factors that were still unknown (and, had nature differed in tiny, almost imperceptible ways, would make such weapons impossible, or at least unlikely in the near term).

The Japanese had a small nuclear project that looked into both of these possibilities. So they were aware of the theoretical potentials, though they also recognized that to develop even the power option would require creating an entirely new industry from scratch, and involve a lot of risk, and that developing a weapons option would be even more difficult.

As for specific awareness of an Allied projects, there is no evidence that anyone in Japan considered it a real issue. The Japanese scientists concluded that even the Americans would have a tough time of making a nuclear weapon. (They were right — it wasn't easy.) They seem to have made no serious effort to find out whether it was true, however. If they had, I suspect they would have quickly figured out that the United States was expending vast resources on the subject — there was a lot of evidence in plain sight, in the form of leaks and mysterious disappearances (all of the nuclear physicists stopped publishing, for example). But Japanese intelligence in the US mainland was terrible, on the whole, so I tend to just chalk up this lacunae to that fact.

I have never found any evidence that the Germans had much of an indication of the American bomb project either. I have written on this question a bit here. Basically, from what sources I have available to me (which are not complete, to be sure), it seems the Germans believed that they were far ahead of the Americans with regards to fission research. They did send information to German spies asking them to look into the question but the very questions they asked indicated that they thought it was small-scale and probably not very sophisticated. (The spies were immediately caught — the Germans also had poor intelligence in the mainland USA.)

The Soviets are a different story. They had indirect indications of an American bomb project — they noticed that the people who were working on fission right before the war suddenly vanished — and they also had volunteer spies (moles) in both the UK and US portions of the fission work. They had an extensive overview of the project as well as knowledge of many specific technical details as a result, from very early on. So it was not unexpected at all for them.

As for other countries, one of my favorite episodes is when a group of Indian physicists showed up to the United States during the war and started asking around to find out where the uranium was being enriched. The Manhattan Project security people quickly found them and asked them where they had gotten such an idea. The Indians (quite indignant about being interrogated) told them it was obvious to any competent physicist that this was something the United States must be doing. They were told to stop asking questions and released.