"I read that Superman used to kill in his early adventures. If so, how many people did he kill, and when/why did he stop?"
THE BODY COUNT compiled by the early Man of Steel was considerable.
1. While attempting to end a civil war in the South American republic of San Monte, Superman kills a military torturer by seizing him in one hand and hurling him through the air into a grove of distant trees. (This is the sequence that Niddle described in his post, mistakenly placing it during World War II.) (Action Comics # 21 [Jul., 1938])
2. Superman leaps into the air to intercept an aeroplane carrying the Ultra-Humanite and his gang. The Man of Steel then allows the craft's propeller to shatter against his invulnerable body, and the plane crashes. The Ultra-Humanite manages to survive, but his henchmen are killed. (Action Comics # 13 [Jun., 1939])
3. Superman deliberately electrocutes J. F. Curtis, an American paid by a foreign power to sabotage U.S. industry. (Superman # 4 [Spring, 1940])
4. The Man of Steel drowns a horde of zombie-like human giants created by evil Professor Zee. (Superman # 8 [Jan.-Feb., 1941])
5. When a racketeer attempts to gun down a girl, Superman kills the hoodlum by grabbing him and, at super-speed, hurling him into the bullet's path. (Superman # 9 [Mar.-Apr., 1941])
6. Superman kills one of Lex Luthor's underlings by hurling him out of a skyscraper window. (Action Comics # 42 [Nov., 1941])
7. The Man of Steel deliberately electrocutes the costumed villain, the Lightning Master. (Superman # 14 [Jan.-Feb., 1942])
And, when the "Superman" syndicated newspaper strip began in 1939, the Man of Steel caused another plane-full of criminals to crash. (See below.)
There were no more killings committed by Superman after the beginning of 1942.
As for the why and when of why Superman stopped killing, the key lies in Whitney Ellsworth, who replaced Vin Sullivan (the man who purchased Superman from Siegel and Shuster) as editor-in-chief of National Comics (as DC Comics was known then) in early 1940.
According to Superman: the Complete History by Les Daniels (Chronicle Books, 1998):
Among Ellsworth's most important tasks was determining a proper code of conduct for Superman. In the first newspaper adventure, Superman had deliberately torn the wings off a plane full of bad guys. The plane crashed in flames, its passengers presumably punished for attempting to do away with Lois Lane. Such melodramatics worried [National Comics publisher] Harry Donenfield: Superman was becoming a very valuable property, one that appealed to a young audience, and the publisher was anxious to avoid any repetition of the censorship problems associated with his early pulp magazines (such as the lurid Spicy Detective). It was left to Ellsworth to impose tight editorial controls on Jerry Siegel. Henceforth, Superman would be forbidden to use his powers to kill anyone, even a villain.
Obviously, Donenfield did not come to this conclusion right after Ellsworth took over as Superman editor, since the Man of Steel still sent an occasional crook to his doom until 1942. But, clearly, the ban against killing was enforced by the early 1940's, since, over in the Batman titles, the same conclusion had been arrived at with regard to the Batman's occasional killing. The last time the Masked Manhunter was seen to have killed was in Batman # 1 (Spring, 1940). And in Batman # 4 (Winter, 1941), the Batman uses a sub-machine gun to wing a fleeing gangster, while the narrative text informs the reader--for the first time--that "[t]he Batman never carries or kills with a gun!"
The timing of the no-more-murder policies in the case of both heroes is so close, it is likely that Donenfield ordered Ellsworth to eliminate any more killing by their two cash-cow characters sometime in 1941.
Hope this helps.