Internation Travel: Questions

Hello All,

I am traveling and wondering

1) Can I keep charged battery in the camera?

2) if not... then do I have to keep it in the Check-in bag or I can just keep separately in carry-on?

3) is there a problem with camera passing through scanner?

Sorry! if this is already answered/discussed somewhere. I will try to search here as well as online.

Thanks in advance,

Ray