Another idea often used is the rule of thirds (https://en.wikipedia.org/wiki/Rule_of_thirds). More often than not, placing your subject dead center feels "too" strong. Most of your subjects have a more "open" side; positioning the open side facing the rest of the frame leads the viewers' eyes around the rest of the image and makes the photo more dynamic.
I remember doing a research paper about photography and another rule I remember was to be careful with the lines and edges in your photograph. You want them to line up and not clash with the borders of the picture.
What if you want an image that imitates the human eye? As it it shows you what a person would see. I imagine that just like with camera lenses what you see varies depending on the distance. I guess it might be a philosophical question but how do you represent how someone "truly" looks?
So is it better to physically move your camera further or closer to your subject then to zoom in and out? I'm guessing there is a trade-off to either extreme and to be as close or far away from the subject as you need to have a strong composition and then zoom in and out minimally for fine tuning, i.e., only use zoom for small adjustments to the frame. I'm assuming this gives you better image resolution.
A good photography guide from NG: https://www.nationalgeographic.com/photography-guidebook/
It's cool that difference camera settings can have really different results and make whatever you're shooting look better. Like how longer focal lengths can make people with narrower faces look wider and flatter, and vice versa
I'm not sure with the professor's suggestion to use digital zoom, since it is effectively the same as taking a full-resolution image and then cropping it later. In fact, you might want to do just that instead of using digital zoom, so you can capture a wider amount of the view and later, in post, play around with framing/cropping your subject. Plus, cropping can be of arbitrary size and shape.
I would like to add that the 1/3 rule is pretty important for photography (https://digital-photography-school.com/rule-of-thirds/). Its not only that your subject should take 1/3 of the image but also that you should place your objects at positions of 1/3, 2/3 of your screen.