[I am going to address the first question because the second part (which I removed) is a very different question.]
Tort law affects health care professionals mostly in the area of negligence, specifically malpractice. Malpractice is a tort that people who hold licenses can be liable for, for example, legal malpractice, or in this case, medical malpractice. Medical malpractice is a failure to exercise reasonable care that results in harm to a patient. Any health care professional who is licensed and who works with patients can be held liable for medical malpractice. Generally, the people who are sued most often for medical malpractice are doctors, but others, such as nurses or respiratory therapists can certainly be sued, as well. There are extreme cases of negligence, such as amputating the wrong limb, and more routine kinds of cases, for example, a failure to exercise reasonable care that results in a post-operative infection. In all cases in which a health care professional is held liable, the plaintiff must establish that there was a duty, that it was breached by a failure to exercise reasonable care, that there was harm to the patient, and that the failure to exercise care caused the harm.
Criminal law, fortunately, does not usually play such an important part in health care. But there is such a thing as criminal negligence, and there are crimes committed in health care settings, for example, theft by aides in a nursing home. Euthanasia, of course, is a crime, and this happens from time to time in health care settings, too.
Contract law is important to health care people for a few reasons. First, there is a contract, implied or explicit, with each patient. Second, people in working in health care might have employment contracts. Third, most third-party insurers have a contract with those insured, and since this is the primary source of most income for doctors, hospitals, and other kinds of health care facilities, these contracts have a significant impact on that source of income.
Generally, it is in the area of torts that most legal impact occurs in health care, but certainly, a knowledge of the other areas of law can be a big help, too.