The first thing you need to do is take your dad to his doctor for an evaluation. There could be medical reasons for why he isn't eating. Lack of appetite
is a symptom of some conditions. He might also have swallowing or chewing problems, which make eating painful or difficult. He may be too embarrassed to mention this. It also sounds like he could be depressed. Losing interest in food is a common sign of depression. Does he seem down or depressed in other ways? Be sure to ask his doctor about depression (which can often be treated effectively with medication), and whether he should be seen by a psychiatrist.
Good for you for taking the initiative with this! Too often, not eating is seen as a normal part of aging, when it's not. It's often a sign or symptom of an underlying condition or illness. It's important to get your dad evaluated, so you'll know the best next steps to take.
By the way, does your dad enjoy the Sunday dinners at your house? If so, maybe you should keep with this wonderful tradition, using a walker or cane as needed? When you talk to his doctor, be sure to mention the fall, and ask about a fall-risk evaluation from a physical therapist. Physical therapists can suggest all kinds of helpful ways to minimize the risk of falling, from exercises to build muscle to mobility equipment. Best of luck to you.