Are there health benefits of a vegetarian diet?

Yes, but... There are advantages to eating a diet that minimizes unhealthy saturated fats, but a vegetarian diet does not limit processed goods that contain white sugar and flour and the diet also allows frying of food and trans-fats. So the plant based aspect of the diet is healthy, but not every aspect including excluding wild fish such as salmon rich in omega-3 fatty acids.
Yes. Studies show that eating a diet rich in whole grains, legumes, nuts, fruits and vegetables provides protection against chronic diseases such as cancer, cardiovascular disease and diabetes.