Barbarossa wasn't delayed by the action in the Balkans (the divisions involved were pulled out in time). The biggest factor in the decision was that the spring had been very wet, making the ground (including roads) too muddy for heavy traffic. The rivers were also too wide, with a stronger current. If the German army was going to be able to use its mobility, it had to wait.
The Germans probably wouldn’t have been able to take Moscow anyway, if the battle of Stalingrad next year was any indication. Meanwhile, diverting Guderian's tank group south led to the biggest victory of Barbarossa.
Arms research mostly continued as usual between 1940 and 1942. The Tiger tank was developed during this time.
During the 1941 Soviet winter offensive, Hitler was mostly right to give the order to stand still and fight. He had been waiting for his generals to stabilise the situation, but they hadn't and as a result Army Group Centre was starting to fall apart. Hitler's order saved that situation (which probably gave him the impression that it would always work, which it of course didn't).
Manstein was never frank with Hitler about the need for elastic defence (not because he didn't have the courage, but because he realised that this was not a time for honesty). Half a dozen times he managed to deceive Hitler about having intentions to advance and afterwards to explain why it hadn't worked, when he actually retreated all the time. After Korsun the gig was up, though.
The first chance Germany had of winning the war was to destroy the Red Army. The second chance they had was to take the oil fields in the Caucasus. If they had been able to do that, the Red Army and the Red Air Force would been forced into passivity. Going for the oil fields was a long shot, but a logical step to take and not a mistake.
After Case Blue failed (the oil fields), there was no longer any question of winning in USSR (especially as the Americans were beginning to turn up). Hitler had to try to go for a draw. The plan was to give the Red Army an epic beating somewhere along the front. The first prerequisite was strong German forces, and the only two clusters of strong armies he had left were around Kursk. The second prerequisite was strong Soviet forces (won't be a battle without an enemy). He waited too long, and the Soviets turned out to be too strong at that point.
In the Battle of the Bulge, the US troops were also many times stronger than the isolated French units in 1940. The terrain in the Ardennes strongly favours the defender. Sending the German armies involved with the Bulge fighting east would barely have been a speed bump for the Red Army. Half a year earlier the Red Army had destroyed 26 divisions in Belarus almost without breaking stride.
But sure, Hitler did send the tank divisions he had used in the Ardennes to Hungary (Operation Frühlingserwachen) where they managed to creep forward for about a week before a Red Army counterstrike broke them and sent them back to their starting point over the next couple of days.
