Hi Heather! I'm not an expert in police officer hiring. I am an officer, and will give you my thoughts.
1.) I think that being on antidepressants might cause you problems (could be an obstacle to getting hired). From the time you submit your application, it could probably take up to six months before you are hired.
2.) You could apply before you graduate if you have time. If you are not from the Atlanta area, the Atlanta Police Department has recruitment trips sometimes. The Atlanta Police Department only requires a diploma or G.E.D. So as far as education goes, you are way ahead.
3.) You would definitely have to be a police officer before becoming a detective. With many departments, you have to be an officer for at least two years before being eligible for promotion to detective.
3.) Surely it is possible, and many officers have decided to work for the federal government after becoming police officers. Regardless of whether or not you were a police officer, you would still have to meet whatever qualifications and requirements another agency such as the FBI demanded. It surely wouldn't hurt if you already have law enforcement (police) experience.
4.) The police academy and then your FTO (Field Training Program) combined are designed to teach you everything you need to know to start out on your own as a police officer. You do not need prior police knowledge to be hired by the Atlanta Police Department.
Your debt shouldn't be a problem if it is from student loans, and you are late on payments or anything. The Atlanta Police Department does have its own academy. The academy is 760 hours of training, and then you receive 240 hours of field training. You will start out at a higher salary for having four years or more of college. Good luck!