Under camera just put the model number like D7100; Once you put the first letter like D you will see a list of all the cameras in the database pop up. The more numbers you put in the smaller the list becomes. When you see your camera just click on it, Be sure to click on "Save Changes" in the lower right corner.
What you are talking about is called "Fine Tuning" there are a number of ways to check it and set it. Depending on what camera you have. All cameras do not have the ability to do this.
Yes, it does. Typically, a lens will get sharper as it is "stepped down", which is to decrease the aperture. For an f/2.8 lens, try shooting a static object at f/5.6 or f/8 and keep the shutter speed faster than 1/200 sec for the 200mm lens, preferably faster by a factor of 1.5 to 2 if hand-holding. If you mount it on a tripod, you should be able to use a slower shutter speed.