exams and driving on shabat for medical students

Dear Rabbi, I am a medical student in the grand cayman islands at St Matthews University.
We are currently encountering a problem with admistration of a written exam on Rosh hashana. Is it permissible to write with a shinuy to take the exam? Second issue , related to the first .
Can I go in a car on Shabbat to get to classes if I do no no action , no opeing door, or driving …
just passive in the transport?
Thirdly , Can I ask someone before shabbat to microwave my food on shabbat when i let him know I am hungry?
There are several of us who are orthodox jews out here and want to know if there would be any heter as we encountering many challenges out here.
thanks for your help !
F S