Harkins, for some reason (rank? position in Starfleet?) had the authority to disengage the primary coolant system, which will cause a warp core breach (presumably because the lack of coolant somewhere will increase temperatures enough to rupture some of the antimatter containment). I will presume that not every clown can disengage the primary coolant system, and that it was something only reserved for chief engineers (or higher, as Commander Harkins may have been) and Captains and such, presumably to be done in case of emergency or technical reasons (moving to a secondary, with the warp drive offline).
A warp core breach might be preventable still, with quick actions, after the coolant system comes offline, and depending on how bad it is breached, part of the ship might survive. On the Enterprise (unlike Voyager), most of it might survive, as it would knock out the nacelles and secondary hull, but the saucer could conceivably clear itself away, even accidentally.
An auto-destruct probably ensures destruction of the saucer and the secondary hull much more thoroughly than a simple warp core breach (although, yes, a breach is probably utilized).
I don't think so. In Timescape a simple core breach causes the total destruction of the ship. A core breach is all you need.