For example, suppose that an enemy casts Time Stop and, while the Time Stop is in effect, walks into the Time Trap that Haer'Dalis set?

Also, what methods can kill an enemy that has cast Time Stop before the effect wears off?

Melf's Acid Arrow? Or some AoE pulsing effect like Cloudkill?

As time is stopped, the timetrap would start when the current timestop is over.

If, after the time trap is triggered, but before the time stop ends, what happens if the enemy casts Time Stop again? (In particular, will the character who set the time trap get a chance to act?)

I suggest finding an enemy that is both immune to Time Stop and able to cast Time Stop, and then try it out. I'd imagine the situation doesn't come up much, however.

You cann't stop time if time is already stopped... you must return to normal time and then you can stop it again.

Indeed, but you cán cast while it's stopped it so it stops again just after it stops...stopping? :P