doesnt really matter, if you asking about battery health thats another thing

just so you know you will have to replace the battery's at some point in its life
but all my gameboys right back to the Original still work perfect, so the system will live for a while

 

turn 3DS's off?

i not sure i understand this term lol
1 i have has been on since launch day and still to this day has not powered off, only reset

 

Doesn't matter it uses lithium ion which has no memory effect.

Just avoid deep discharges and you should be fine (when it shows low battery plug it in) however inversely remember to run it on the battery sometimes leaving it trickle charging can mess with the battery controller chip and make it drop outta sync with the real battery level.

So really just use it, occasional deep discharges are fine as long as its not every time and run it on battery only sometimes

Edit: Oh, Your Device will charge slower while being played and charged at the same time if you want to charge it faster turn it off