There isn't really a right or wrong answer to any of this--it really boils down to personal preference and what you want your scene to look and feel like. For example, the symmetrical shot you used for the school classroom (if that is what it is) works very well since schools are often very regimented and controlled environments, so it makes sense to reflect this using cinematography. On the other hand, if you want to convey chaos and ambiguity, a disorganized and asymmetrical frame would be a much better choice. Symmetrical frames also lend themselves well to visual comedy, I think, since there's something inherently funny about people or objects lined up in a certain way.
You could also play with these expectations as well, by, for example, having a very symmetrical frame and then have a character walk into the frame and disrupt the symmetry to show he/she does not fit in. It really depends what you're going for--the cinematography should fit the scene you want to convey. Either way, it's best not to overuse one particular style. I remember watching The Grand Budapest Hotel, and becoming annoyed because the movie overused symmetry and head-on/profile shots to the point where the cinematography and editing felt choppy and mechanical, which disrupted my immersion in the story. (Having said that, I feel like this film has grown on me considerably since I've seen it, so I'll likely feel very different about it if I watch it again sometime.)
Also, if you want to improve your cinematography skills, I would highly recommend looking at this YouTube channel, if you haven't already (it's been mentioned on this site a few times already, so you may have already come across it).
Retribution (3rd place in BRAWL 2015)&Smeagol make the most of being surrounded by single, educated women your own age on a regular basis in college
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