If you have strong myopia, or nearsightedness, full small glasses frames are best the choices.
As we know, the eyeglasses lenses for nearsightedness are thin in the center and thick at the edge of the lenses. So, the bigger the lenses, the thicker the lenses edges. To make the lenses look thinner, small rimmed frames are good choices because they need small lenses.
Yes, absolutely yes. Personally, someone who wore very strong prescription lenses for many years really need to be looking at the frames for the smallest lenses that he can accept. The center of the strong prescription lenses is thinnest in a strong prescription lenses and it will become thicker and thicker moving to the rim. If you choose the big glasses frames, the rim of the glasses will look thicker than the small glasses frames.