Can someone/something other than the pilot trigger the ejection seat?
In a word, yes.  

There is a switch which controls this and the default position is "both".  If any handle is pulled (pull down over the face or the one between your legs), then both seats fire.  If solo, the switch is turned to "solo" so that the rear seat is not ejected and the front seat gets to leave a little bit quicker.  If the switch is left on solo, and both seats are occupied, then each crew member can eject on their own.  

You would also have if set to "solo" with an untrained passenger in the back.  You wouldn't want someone getting a bit excited and firing them both out of a perfectly working jet.

See this question about what happens, and this one to understand why you won't hit the canopy.

As far as I know, there is no computer controlled ejection system.  I don't think anyone would trust it to know better than the crew when it's time to bail out.