The drone in question is a DJI Phantom 3 Standard.
- Can I fly with a drone at all?
- If yes, carry-on or checked bags?
- Do you need to declare it?
- Do you need to take it out of bags at Security X-ray like laptops?
I've flown within the USA, to the US from Canada and Europe, and all over Europe without issues. Here are a few tips:
Many airlines now have a drone specific page on their website - search using something like "can I take my drone on British Airways" to find it. Print this page and take it with you when you fly.
There are likely to be limits on the amount of LiPo batteries you can fly with - at one stage I checked and it was three for my specific model on that particular airline, based on size.
Your LiPos always have to be carried as hand luggage.
It's advisable to discharge your batteries to around 1/3 for safety reasons. Take a look here for other handy LiPo battery handling tips: http://thedronegirl.com/2015/02/07/lipo-battery/
It's advisable to store your LiPo batteries in a LiPo bag (available on Amazon, ebay, etc).
Some countries don't allow drones to be imported and this could apply to passengers in transit. There's a pretty good list of applicable laws, by country, here: https://uavcoach.com/drone-laws/
I've never had a problem, other than a couple minutes delay at security as they looked over my drone (I've flown with a Phantom 4, Mavic Pro and Mavic 2 Pro) and on only one occasion did I need to nudge their approval with production of the printed "can I take my drone on __airline name____" page.
As long as the remote control and the drone are off (they would probably consider those as radios/remote controlled vehicles, which are not allowed to be used in flight) I don't see an issue.
You will need to register the drone with the FAA in order to fly it, and I might be wrong, but you may need an address inside the US as part of registration.
I have also checked the TSA website's tool "What Can I Bring?" for "remote controlled helicopter" and it said it could be in your carry-on or checked baggage.
However, I would avoid calling it a drone in the airport, because it says that drones might not be allowed and groups them with hoverboards/self-balancing scooters because of the battery.