Well C6, with a response like that you're not likely to get much more help! EAGLE (and the others) made some very good points, the last one might be particularly relevant - remember that you are there to teach/protect rather than to demonstrate your superior abilities!
The "how to take over" question should really have been answered by your instructing experience to date and also during your aero-instructor course. If you always take over too soon the stude doesn't learn, if you wait too long you might frighten the stude or bend something. Every situation is different but if your stude should be capable of sorting the problem (you've taught them) and you aren't approaching any limits (yours, the aircraft's or altitude) then leave them to it.
In the UK we have Beginners and Standard (rather than Sportsman) these are invariably taught dual. The higher levels are taught by mixtures of dual and observed.
As for Avalanches, etc: I don't teach in Aerobats but if you can flick (snap) and loop I don't see why you can't do an Avalanche (or multiple separated flicks - or stall inverted)?
Finally, I don't wish to insult your abilities, but if you can't see the benefit of a parachute when teaching aeros you might have more to learn than you realise! I (and many others) wear parachutes and bonedomes whenever possible - certainly for spinning and the more interesting manoeuvres.
Fly safely and give good value!