Make sure (absolutely certain!) that your bag is within the limits set by the airline as far as measurements and weight go - they can insist it goes in the hold if it's over. However, if it's only JUST over the limit of weight, you can stick a couple of lenses in jacket pockets for the weigh in then transfer them back into the bag as soon as possible (possibly best done out of sight of the weigh-in desk but it was one of the girls there that told me to do just that a few years back!)
The camera and lenses will have to go through the usual scanner and they might want to look at and swab the bag's contents. Doesn't take very long for them to do and it helps pass the time. Any LiIon batteries should (MUST!) be in hand baggage rather than in the hold. Nothing to worry about. I always stick leads and chargers in the hold baggage to reduce the weight of the hand baggage. If you have them, stick the plastic covers over the terminals of any spare batteries, if not, maybe a piece of insulating tape could be pressed into service. (I'm not aware of any short circuits happening in camera bags but I wouldn't want to be on a flight where it occurred...)
Pretty sure that he regulations for internal flights are the same as international other than the ID requirements. If in doubt, check with the airline concerned.