Brightspace/D2L email is internal only. This is to prevent spam from reaching the learning environment.
However, emails can be sent out to external addresses. You can also have your emails forwarded to an alternative address by selecting your username at the top right in Brightspace, selecting Account Settings, then the Email tab.
Please see your instructors syllabus for how they wish you to contact them whether to contact them through Brightspace, or their regular @mga.edu account.