Gitterdun:
Most MRIs can be performed without sedation provided the patient is cooperative and can hold still during the image acquisition. This can be a rather long time, depending on the exam being done, on the order of 30 minutes or more. As stated previously, sedatives are often used for people who have difficulty being in the bore of the MRI machine, which is rather like being in a torpedo tube (open MRIs tend not to provide the same image quality as a conventional MRI). Children are often sedated, for obvious reasons. If sedative medications are necessary for your exam, then you should refrain from diving as instructed.
The "dye" mentioned is also called a "contrast agent" and generally consists of gadolinium. Depending on the type of MRI being done, it can greatly improve the diagnostic utility of the examination. This is usually given as an intravenous injection, although on occasion it is injected in other forms, for instance as a liquid into a joint space for a joint MRI.
Discuss your concerns with your doctor, and ask them to verify any persistent concerns with the radiologist responsible for your MRI. And don't forget to leave any metal items and credit cards in the locker they'll provide for you!