Typically during the exam the system freezes your computer so that you can only work within the exam software; there are other systems that may register sound or any attempt to access files; and of course plagiarism is a big deal in college so they have software that checks papers.
What classes would you take through DE and what would you take through your regular HS? Would your HS provide you with a quiet space&a computer to complete these online classes during the school day? What are rigorous alternatives to these classes?