In career mode you are given your original assignment and apparently you have been completing it. When you get the gray star you can call in and receive a new assignment, Captains Log button lower right corner of the screen brings up the clip board and there is a button to report in.
It will be a patrol mission not an agent drop type thing. You can keep doing this over and over till you are either out of torpedoes or low fuel than return to base and end patrol.
Early in the war it is best to complete two or three missions per patrol as you will be given a new boat sooner that way. Once you get a new boat you can just complete one assignment and then sail where ever you think you can find enemy shipping. Sinking ships is more important than completing missions.
As far as the medals goes, when you click on the Medals box your medals are shown on the left side of the screen.
Welcome to the boat mate good luck and good hunting.
Magic