Your sentiment and emotions are understood, and noted.
never the less, my thoughts as follows---
#1. Situation dependent. How fast were you going, and how far from the light/intersection, is the key.
#2. "Prudent" is one thought, good judgment based on situation is another. In the case of worrying about traffic behind you, is also based on individual good judgment while approaching an intersection. Meaning, you should always be prepared for the light to turn yellow, hence a following Red Light. So, in reference to following traffic (Someone in near-vicinity noted in your rear-view mirror), and approaching an intersection, one must prepare to stop, and ensure appropriate distance for stopping is conducted, accordingly, etc.
#3) This question (again) refers back to your emotional distress, in reference paying a fine, money out of your pocket. Address the issue objectively, taking the financial factor out of the equation, and you might consider this in another perspective, and prevent any future situations, and possible road-rage that might transpire, from this incident.