Can a second floor exterior egress stairway go past a window on first floor on way down?
Yes, but depending on where the window is relative to the stair and its dimensions, you may need a proper guardrail installed and/or the window would need to be made of tempered glass. This is the same requirement for low sill windows where someone could potentially fall through the window at normal floor level, except the stair treads can be considered "floor level" for determining application of the rules.

There can easily be local requirements in addition to IBC requirements.