1. While much has been made of the theoretical physical effort at Los Alamos, without the Oak Ridge, TN and Hanford, WA chemical-physical production lines for uranium-235 and plutonium, bomb production would not have been possible.
2. These efforts required vast inputs of energy, mostly provided by hydroelectric projects such as TVA for the Oak Ridge uranium effort. It's highly implausible that such efforts would have succeeded in wartime Germany no matter how many resources were diverted to them. One bombing run would have wiped out the whole enterprise - and of course, neither Oak Ridge nor Hanford were subjected to aerial bombardment.
3. The Germans apparently were more interested in a nuclear rocket engine or some such than a nuclear bomb, by most accounts I've read. Also, their heavy water project in Norway was effectively sabotaged.
Note also, many scientists involved with the bomb project quit as soon as they learned Germany was defeated and so the rationale of beating the Germans to the bomb no longer made any sense.
FDR, if he hadn't died early, would almost certainly have rejected the use of the bomb against Japan, for the same reasons that he rejected the use of poison gas against the Japanese holdouts on Iwo Jima and Okinawa. If the Japanese had simply been given the option to retain their figurehead Emperor, they'd have certainly surrendered rather than accept the occupation of northern Japan by Russian forces in a replay of East Germany.
Isn't history fun?