I fly pretty much every week, all over the world. I usually put all my liquids in a ziplock bag and take it out and send it through the scanner separately. I normally carry 2 mods, a Provari with a tank/carto set up and a Mech mod with a Nimbus dripper fully assembled in my back pack. In the past year I have been asked several times what it was, a few TSA said "is that an e-cig in your bag" and one time I had to disassemble the Mech mod and have it swiped for bomb residue (Washington DC). Nothing that has ever happened to me has been more than mildly annoying and for the most part the airport security are pretty much aware of e-cigs.
Now as far as vaping on the plane I would only do it in the bathroom. I have had several issues trying to vape in the Airport or on the plane. Their reasoning is that it looks like smoking so it will cause a big fuss and no one is going to care about your 10 min explanation of how its vapor and only contains trace amounts of nic in the clouds you exhale. I try to be as respectful of my vaping as I was with smoking around people who do not do it. Better off just holding off until the flight is over.