A simulator is a software application running on some host platform; there is no reason in principle why it shouldn't include simulation of interrupts, etc; in fact, the Keil simulator does provide an interface whereby you can provide simulations of your own custom hardware.
Of course, developing this simulation could well be a major project in itself...!

Coverage analysis provides you with a report of how much of your code has & hasn't been executed; how often particular parts of it were executed; how long they took; etc.
So it's closely related to TRACE, and probably relies on the same underlying support, but not quite the same.