Are emergency actions an appropriate part of a captain's briefing in a light aircraft?
It sounds like you are covering the safety material you need to from a regulatory and good sense approach. Trying to convey an emergency exit briefing during an emergency is not going to work, you need to give it all at the beginning. If you get an engine fire on startup you need your passengers to be ready. 

I find that people appreciate that you give a briefing as it shows a bit of "professionalism" that re-assures them, rather than scaring them it shows you know what you are doing. I do cover the same material, and I usually do it slightly tongue and cheek in the similar manner as a commercial airline. For example when I talk about emergency exits I point to the doors to the left and right, then say something like "if there is an exit behind you then things really have gone wrong". That's just my personal style, there's no hard fast rules on it. If people decide not to fly with you after your briefing maybe you are going about it wrong though. 

The approach I take with small children is different than that which I take with adults. The first flight in a light airplane is a very novel experience for anyone, with kids I explain what the experience will be like a lot more than adults. An adult will understand what you mean by climb usually, but saying "the airplane will lean back a bit and we will go up" makes more sense to a little kid.