Safety of Lipo batteries
1) Yes, defective Lithium batteries may burn or explode, but properly handled and protected, they are safe.

2) Not knowing what exactly you're doing:


Riggid packaging, so people can mishandle the battery without blowing up.
Prevent short circuits, deep discharging and overcharging with proper protective circuits.
Train your teenagers what happens if you treat a battery wrong. There are tons of videos on youtube. Don't do plain theory, but also add explosions and burning batteries. Teenagers (and adult engineers) love explosions.


3) I would recommend staying with Lithium Ion batteries. Best you can get on the market and as long as someone knows what they're doing, they're pretty safe.