Could be that they see the spark case as an extra carry-on luggage? Just put it in your backpack, that should do. I usually travel with my Spark in my handluggage, batteries detached, never had any question about it. Also had it in my checked-in luggage with batteries in my carry-on, no...
Picture is quite a bit on the safe side, seen that before with DJI. Have a look at the AirMap-app, I find this to be more accurate/precise.
As for security, batteries in the carry-on luggage, the drone itself wherever you want it in your luggage.
My experience: Nobody cared, inbound nor outbound. I had 2 batteries in my handluggage, went through the security scans without a problem. I travelled within Europe (Schengen), might be different when flying in from outside Europe.
I had a Tello for a week, before I exchanged it for a Spark. If I remember correctly, yes, it does land where it is at that moment, as it doesnt have GPS, so it wouldnt know where to go elsewhere.