You can check
e-liquid but take some on board with you as well just in case. It never hurts to have backups whatever the case. Just don't have any bottles bigger than the allowed size for liquids and put them in the baggie with the rest of your carry-on liquids. When I flew to Germany last year, I checked two 30ML bottles with the rest of my toiletries and carried two of the same size bottles on board plus a few dropper bottles full. All of those were in my baggie with other liquids (contact solution, etc), and no one batted an eye
through three countries.
For your
device and cartomizers, I agree with Ray. Take them with you. TSA is fully aware of PVs, so at most, you might get a curious agent and be asked what it is. My advice: disassemble it before going through security. The only time I got questioned was in Munich. I was in a hurry and forgot to take my cartomizer off. So it must have looked a little suspicious on the scanner. (It was in my backpack.) I let him take it out, told him what it was, and he sent me on my way.