I am envious of the environment where you never saw somebody trying to bug feature request as a bug. I do think in a lot of cases, it's a judgement call...or a habit where problems perceived as bugs by customers are swung under the carpet as features as bug is only defined as "deviation from requirements".
Fair on distinction of severity by customer vs priority by team, although I am used to make a distinction between support ticket by customer and issue in engineering team's queue.
Lead implies either managerial or technological leadership and especially in mature organisations, I've seen both.
My experience with management by bug statistics is...very inconsistent as it motivates people to game the system...and boy I've seen that a lot. I do agree trend knowledge helps, but I am not sure it's worth the side-effects and work.
Of course, a flavor of this depends on context (and scale). It is very different if you have a single-instance SaaS, distributed system or images shipped to air-gapped systems.