That's the part I was most interested in. Had there been a Reich Ministry of Armaments and War Production early on, could the German economy have better compensated for the early shortfalls such as gasoline production, coal production, etc?
They could have coordinated better to prepare for the war. However you have a problem when you don’t know when it will start exactly. To Raeder Hitler promised no war until mid 40s and Raeder prepared accordingly. Hitler himself miscalculated and didn’t think Britain and France would be willing to go to war over Poland. So in that regard the stockpiling of resources may have been increased but it would not be in sufficient quantities for war in 1939 unless someone from the future tells Hitler when war would start and even then its questionable if he would tell anyone that due to fear of leaks.
Could Germany have produced more tanks and such? Certainly. It couldn’t fuel them however so that would be a waste considering the incredible pace of armor development over the few years of the war, what was state of the art in 39 was practically a death sentence to climb into in 43 or 44.
Can Germany produce more fighters? Yes. It still couldn’t produce high performance ones like Mustang because it didn’t have access to high quality high octane fuel.
Can Germany have more trucks? No. They require rubber and armaments ministry in 41 or 42 recommended further demotorization of Wehrmacht due to lack of it. Germans used horses for a reason.
What armaments ministry could have done is enforced standardization from day one, and made weapons development projects based around economy’s capability to support it and manage it resource wise. No sturmtiger, earlier E program etc.