Hopefully to answer your questions .. .. ..
1) Hopefully! My youngest acquired a DS when he was 4 but .. .. .. he's broken the original one by accidentally dropping it in the toilet (it's a long story). As the price of brand new DSLites has come down to around £85 it's not so painful now if it happens again .. .. ..
2) aha! second hand! Good thinking! It should come with a charger and a stylus. Check the hinge areas for hairline cracks then open it up until it clicks, place it in the palm of your hand and gently bounce your hand up and down. The top screen should not flap about. If it does the hinges are on their way out so look for another one.
3) You don't
need any extras, but some people put screen protectors across the touch screen.
4) Don't drop them in toilets .. .. .. ..