A: Annoying things ophthalmologists do
The short answer is "Yes." I always tell my patients that they are in full control of their eye care and their visit. That being said, I also advise my patient that we perform the tests you mention for good reason. We are looking for problems in your eye that could result in vision loss. If caught early, many of these issues can be prevented or at least slowed. The "air puff" test is checking your eye pressure (an important measurment for the detection of glaucoma). This information is critical to assessing your general eye health, and should be performed at every visit. However, there are other ways of performing eye pressure checks, so if you absolutely hate this test, ask your tech or physician to perform pressure checks another way. However, understand that numbing drops are needed to measure pressure with those other instruments.
Numbing drops also help if a small procedure needs to be performed. The nerves of the cornea are very sensitive, and so numbing is a way to keep you comfortable. The numbing should only last 20-30 minutes, so you should actually be feeling normal around the time you check out.
Dilation is a critical part of assessing your eye health. It allows us to see all areas of the retina and optic nerve. With dilation we are able to see if your eye has diabetes, glaucoma, macular degeneration, freckles and many other eye disorders. Without dilation, the view to the back of the eye is limited and important issues can be missed. Fortunately, in most healthy adults the dilation only needs to be performed every 1-2 years.
Also, don't hesitate to call the office beforehand and inquire about the need for dilation and pressure checks at your visit. They will often be able to provide you with an answer, or if they cannot answer themselves, they can ask one of the medical staff if dilation would be needed. That way, you can plan accordingly or reschedule if needed.