this might be an interesting read for you: Teaching Methods / Proposed Outline at Sensei's Library
my PERSONAL opinions are:
I think it is best to start on 9x9 until one fully grasps the rules and concepts. It seems pointless to me to spend half an hour (or more) playing a game you do not understand and have no chance of winning. Move to a bigger board when you both agree. I am sure your “student” has own opinions. Explain the differences, warn about the time differences, and of course try to motivate a bit (19x19 is awesome). She will surely want to try for herslef soon. 
Or consider 13x13 as a compromise before going all out.
Certainly not. Of course you should be able to win to keep the authority of a techer, but try to win by a small margin (also a good practice for you). Try not to capture groups that are too big (very frustating). Alternatively give enough handicapes to keep it a challenge for you and winnable for your opponent. The progress will then be immediately appareant to her and she will stay motivated when she discovers that she needs less stones to beat you now. Try to refrain from playing trick moves. Play simple solid moves that are easily understandable. And of course do not forget to highlight good moves (not just pointing out the mistakes)
Again, ask if that’s okey for her. I personally like being told my mistakes right after I make them, when I still remember the context and what my precise intentions were with that move. I feel like it is then easier for me to adjust my ideas.
Introduce the idea of shape and do not forget some fun-facts to keep it fun 
