Basically, my question is about trying to understand what the common solider understood about Germany's larger war plans. In July/August/September of 1940, did German soldiers, pilots, and sailors believe the war was going to be over soon, that they'd invade Britain soon, or that they were going to soon be embroiled in eastern Europe?
No they would not. In fact most of them expected to be able to return home. It was widely belived that with France out of the war, Great Britain would sue for peace. This was not the case, mostly because Churchill, who followed Chamberlain after the disaster at Narvik, refused any attempt to try to find out how favorable such a peace would be. In britain there were a strong belief and fear of a German invasion, but this was probably unresonable as the Germans lacked both airsuperiority and the naval force for such an operation.