abc and xyz make sense because they lie on opposite ends of the alphabet, so if you need more variables for either sets, there’s a lot more room to maneuver. If you’re looking for the history of these variables in the context of Cartesian coordinates, I’d start with looking at Descartes’ work. This whole system originated from him, so if he used xyz, then that must be where it came from.

I’ve seen p and q used in various contexts. For example, they could be probability distributions (e.g. KL(p|q)), they could be two points. In these scenarios, we just use p because it’s the first letter of whatever they represent, and q comes after while looking similar so it suggests that they’re the same type of mathematical object.

For indexing, it’s what we commonly use just because we call it an index. You’re not counting or tallying things. It’s a reference to a location in memory. But if you are counting, then c makes perfect sense and I’ve definitely used it in that context. I’ve also used t for indexing if that index represents time. But if there’s no other meaning associated with it, then it’s just an index, hence i.