I couldn't begin to explain the square lens question but I have always wondered why very few lens shades are made rectangular. A round design wastes valuable shading that results in flare when shooting toward the sun or other small/hard light sources. An old Leica camera I had the pleasure to photograph with had one. Doesn't seem like a difficult engineering problem to me.
You can use your LCD screen like an old fashioned hand held meter. Set your camera to manual mode, point the camera toward the scene and adjust shutter or aperture until centered reading is achieved. You wont get pinpoint accuracy since you can't be certain of exactly what the camera is pointed to but it will be close enough for most applications.
Thanks Pat! Don't photograph men's shoes too often but these were just too cool to leave alone.
Go to the PPA site and take the sample CPP (Certified Professional Photographer) test. Although it is more portrait oriented it will give you an idea about what you need to know as a pro photographer. Having said that, and having scored very high on the actual exam, my actual photography needs more improvement than ever. The art and science continues to evolve. We all need continuing education and practice. The important thing is to never be satisfied.
I seem to recall learning that concept after reading the old Time-Life series on photography back in the 70's. There may be a graphic showing this relationship. Try "The Camera". Unfortunately I lost my copies years ago but those books can be bought used for only a few dollars each on Amazon and although they're all about film, the basic concepts of lens construction, design and focal relationships are of course still relevant.