If I try to kill a face down creature, can my opponent save it by flipping it?
Yes morphing will save it because your opponent will get a chance to respond after you cast your spell and there is a ruling related to morphing the card that would apply here.


  Any time you have priority, you may turn the face-down creature face up by revealing what its morph cost is and paying that cost. This is a special action. It doesn’t use the stack and can’t be responded to. Only a face-down permanent can be turned face up this way; a face-down spell cannot.


So this would allow him to morph it and turn it into a 0/5 creature which would save it.