Student role cannot award badges, even with the award badges permission set to Allow. I may have missed a permission setting, so have reproduced sequence of events below:
As admin, ensure the student role has capability "Award badge to user" is set to Allow.
As a teacher, add a badge to a course, and set release criteria to be manual, with student role to assign. Release the badge!!
As a student, login, go to course, got to Administration block - you'll only see your Badge preferences and your Backpack settings.
How does a student get to the award badges area?