Additional question: Did the Wehrmacht recruit anyone that wasn't considered German? I was under the impression that foreign nationals willing to collaborate were organized in the SS.

It depends on what German occupied territory you are talking about. Eastern European countries with a high population of ethnic Germans had all of their volksdeutch(German people) conscripted quite early, around 1942-1943. These men were conscripted not into the Wehrmacht, but into the Waffen SS, due to the desire to make the SS a multinational force for the fight against communism. As the years went on, the definition of what a German was ethnically became more lax and even more people were conscripted from other countries.