The UK was aware because it had been in communication and, eventually, cooperation with the US. It definitely affected their relationship: Churchill really wanted to be part of the Manhattan Project because he feared that the US would dramatically surpass the UK in world importance and scientific knowledge if he did not. The Manhattan Project advisors told FDR that they didn't need the UK's help at that point, but FDR was convinced by Churchill (who appealed to their "special relationship" and cultural connections) to let the UK take part anyway.

The Soviet Union was aware of the US program because it had several "moles" (volunteers within the program who agreed to pass information on to them as spies) within the Manhattan Project (a dozen or so total, though only about four were what we would call really critical). It did affect their relationship: Stalin especially did not like that the US, its putative ally, was keeping such a thing secret from them. It has been argued that this played a role in why the Soviets did not trust the US in the postwar and would not work towards banning nuclear weapons, and instead put their efforts into developing their own weapons.

No other great power had a clear idea of what the US was doing. There were rumors and suspicions throughout World War II about atomic bombs on all sides, but none of them were taken very seriously in most countries. The surprising thing about the US development of the atomic bomb was not that it was researching it (the basic science that the atomic bomb is based on was public knowledge in 1939), but that it managed to accomplish it so quickly (that is, that they were devoting mammoth resources to the task). Scientists in France, Germany, Italy, Japan, and many other nations knew about the possibility of nuclear weapons; they just didn't realize they would be there so soon.

On the British reactions, see Farmelo, Churchill's bomb. On the Soviet reactions, see Gordin, Red Cloud at Dawn.