All rechargeable batteries should be in carry on. For persons carrying hobby equipment batteries should also put the batteries in lipo bags as carry on, this would apply to hobby aircraft such as drones.
Yes you can
Yes you can but make sure it's not in your checked bag. Keep it in your personal item bag or carry on and if your carryon gets checked at the gate be sure to remove the charger from the bag before checking it.
Yes sir
You can bring it, but has to be in your carry on bag
As long as u don't put it checked bags
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