I recommend not a good idea because they may not be as protective as ones that have never been used.
Never buy a used helmet. It's dangerous because if it has already absorbed heavy shocks it will be useless for you. You don't necessarily see the damage on the outside or inside of the helmet, it is only visible if you tear it apart.... but this way the helmet is still useless because it's broken.
No, never. You can't see the damage done, you can't see if the protective padding has been compressed from a fall. It doesn't have to be broken on the outside for it to be ineffective and useless. It's not worth it for a few euro/pound/dollars cheaper.
I think it's fine as long as you look into it and make sure it's a good one. It certainly is a matter of preference though so do whatever you feel most comfortable doing
I would avoid! People say no falls but you never know, even if they haven't fallen off in the hat they may still have bashed it.