Richard Overy lists the number of Germans killed by Allied bombing at 353 000 in The Bombers and the Bombed: Allied Air War Over Europe 1940-1945. The bombing of Germany was carried out chiefly by RAF Bomber Command and the United States 8th and 15th Army Air Forces, so no, the RAF was not solely the force bombing Germany.

As to the moral/ethical question, this is a tricky area, especially when concerning what both sides were trying to achieve with their bombing, and what that bombing actually achieved. In terms of damage to German transportation networks, waterways, fuel supplies, and industry, and the forces that the bombing tied down in Germany, along with the irreparable damage that the Defence of the Reich Campaign did to the Luftwaffe, the Allied bombing offensive did play an important role in the defeat of Germany. /u/Domini_Canes might be the person to ask about the moral/ethical quandaries.

Thanks for the summons, /u/DuxBelisarius. Since you covered it so well I can't add anything on most of the question, so I will merely address this portion:

Were the air raids any more or less ethical than Nazi bombings in Britain?

That would depend on which Allied bombings we would compare to which Nazi bombings of Britain. Luftwaffe attacks on airfields and radar facilities would be seen as acceptable within the confines of warfare by most any standard--poison gas was not used and the attacks were focused on military assets. Later attacks on British cities (either as part of the 1940 "Blitz" or by V-1 and V-2 attacks later in the war) were far less discriminatory. Allied attacks varied as well. Daylight attacks could be highly focused. The August 17, 1943 American raid on Schweinfurt was an example of a focused attack. Given the imprecision inherent in WWII bombing attacks, killing roughly 200 civilians in that attack means that a relatively small area was struck that wasn't the factories themselves. Other attacks (famously Dresden, though Hamburg was more deadly) were focused on killing civilians, particularly with the use of incendiary bombs.

There were contemporary objections to aerial bombardment, particularly from Pope Pius XII who continued a papal tradition of denouncing the practice that dated back to WWI. This approach was mainly based on the concept of distinction from Just War theory, meaning that military forces should distinguish between combatants and noncombatants as much as possible during the fighting. Area bombardment of cities certainly did not practice distinction. Others justified this practice by asserting that enemy civilians were part of the war effort and therefore were legitimate targets. However, some of those who backed Allied bombing efforts also publicly condemned earlier bombings such as Guernica, Warsaw, and Rotterdam as well as London--a hypocritical position to say the least. Some did maintain the legitimacy of area attacks on civilian targets throughout the war, but ethical support for such tactics became more muted after the unprecedented destruction wrought by firebombing raids and nuclear bombs.

The other two gave very good answers. An interesting footnote however is that the Soviet Red Air Force also carried out at least one raid on Berlin in August 1941. The effects were minimal compared to the RAF and USAAF raids.