AtownDown,
That's an awesome idea that I think carries a LOT of potential. I am by no means an expert or authority to be quoted, but IMO the TRX is a great way to introduce strength training and the benefits of exercise to children. As for your questions, some angles you may want to pursue:
1) Benefits of using TRX with kids include introducing fitness and healthy lifestyle choices to them early (many studies have suggested that learning the benefits of exercise early encourages healthy lifestyles throughout life), TRX is fun and challenging and will likely encourage class participation, TRX is bodyweight dependant and therefore safer than weight training for developing youngsters.
2) Demonstrating the TRX should be easy enough. To safely introduce it to your students, I would suggest using some of the more basic exercises (suspended side plank on hands with taps is probably not a good one to start with!!) and starting with the most regressed position until you (and they) are comfortable progressing the movement.
3) Again, I'm not an expert, but I don't see any dangers with the physical development of children that are using the TRX or other forms of strength training. Heck, all those gymnasts in the olympics are under 18 and most have been training since 3 or 4 years old!! That said, the TRX does demand a lot of core strength, which many kids probably have not yet achieved. To that end, I would use simple exercises and progress the movements slowly. By encouraging the development of their core strength now, you will be setting them up for success later in life by making them less injury prone and better prepared for heavy lifting when (and if) they choose to pursue competitive sports or weight training.
4) I'm not sure where you are in the world, but if you are a US educator I'm sure that you have seen a rise in childhood obesity. Strength gains aside, encouraging healthy activity and reducing this growing (no pun intended) problem of overweight adolescents would be enough to convince me!
5) I don't see a problem with using the less challenging exercises with elementary aged children. There are probably professionally certified people on the forum that could better answer this question though, specifically with regards to the appropriate age to start training.
GOOD LUCK! I really hope you get your program approved!
"Teaching is only demonstrating that it is possible. Learning is making it possible for yourself." - Paulo Coelho