How do you know if you passed Training?
 

Well, I went through the first three training missions and I GUESS I passed them. Each mission ended and asked me to click NEXT. The main training screen does not show that I passed these three missions, like it did in SH3. Am I missing something?

No, just think of them as practice missions, not classes. Therefore, it's normal that you aren't seeing "PASSED" on the missions.