LGTM

I wonder if such a situation could occur if we were in some huge medium where Cherenkov radiation could occur

Hmmmm, I guess that the premise was probably wrong then, since the object necessarily has to have mass and travel slower than c (I mean, a massless object would be constrained the by c anyways). The gravitational lensing is a good addition! I have no idea how I forgot, but I remember a hs physics class where this came up for new telescope images

I always just used my left hand with the thumb and pinky as the y and x axes respectively, then the in-between fingers just help me visualize which "point" is higher (we only have two options to choose from if they're not equal anyways)

Absolutely agree, lowk a programmer must've done it else I don't think I've met a mathmematician (or maybe, not crazy enough ones) that ever preferred redefining variables (esp in pedagogical material!!!!)

What do you want to learn PDEs for? It's not my strong point, but I've heard high praise for Partial Differential Equations by Stanley J. Farlow. I found it useful in my undergrad, else I think I could have died in analytical mechanics