Hi @micke,
Thank you for two good questions. We do not have any specific recommendation, but it is good that you do not make the buttons too small. For some people, the gaze point signal can be quite noisy. The good news is that the EyeX Engine has some functionality to filter the data and use object tracking/snapping to make it easier for the user to select the correct button.
One design you can think about, which is more important than the button size, is where to place the menu. If you place it in the top of the screen, there will be a larger angle between the eye tracker normal vector and the gaze vector, which can make the gaze data even noisier. A suggestion would be to have a triggered menu that pops up when you press a key and uses the center part of the screen to present the menu alternatives, similar to a “command rose” in computer games. But it depends on your use case if this is possible alternative.