Harry Truman did not give Japan a chance to respond and surrender before dropping the second bomb.
Yes he did. The Japanese War Cabinet was unable to meet because one of its members had "more important business" elsewhere, and therefore did not respond. When the cabinet finally convened arrival of the news of the bombing of Nagasaki did not alter their deliberations.
A group of young Japanese historians (young in then 1960s that is) called The Pacific War Research Group had access to such of the seniors who were still alive and to such papers as survived. Their book, Japan's Longest Day, documents the attempted military coup that the army launched to prevent the post-Nagasaki surrender. Its findings have never been seriously questioned; it makes it quite clear that it was only the impact of Nagasaki on Hirohito that led to a surrender, and it demolishes utterly the "negotiating with Russia for an orderly surrender"; even had Stalin (Stalin!) been willing to agree to this, the same problem of getting support in the war cabinet would have arisen.
Estimates on the cost of lives of the war continuing are hard to make, because it could have taken many paths. However, deaths from starvation in Japan were accelerating (not least because of Operation Starvation, the mining of harbours and coastal waters) and would have accelerated still more once the US had been in a position to interdict road and rail bridges, in the manner of the Transportation Plan in France. Conservative estimates would have a million a month dying of starvation by the end of 1945: a Hiroshima every four days. The Army had reserves of food, so could, and would, have fought on. Japan would have been reduced to the stone age before it ended, and even then hundreds of thousands of Allied troops (not to mention civilians in Java, Sumatra, Korea) would have died.
Even after Korea, Vietnam and two wars in Iraq, America has not had to make any more Purple Hearts: the stockpile it manufactured for Downfall/Olympic was so large that seventy years later, people given Purple Hearts for wounds in the field are given medals made in 1945.