I've flown to a few different countries with them and have had no problems. Might be good to check and see how legal they are depending on where you are going.
When I do go I have my batteries/devices in the front pouch (which is clear) of my carry on bag, that way they can see what it is. All juice I have is labelled and I put it in ziplock bags, take it out and keep it under the limit for liquids. You could put them in your checked luggage, but I usually travel light.
Going anywhere from Canada is usually fine, it's coming back into Canada that is usually a problem. I usually try to plan to use just enough, or have just a little left over by the time I come back in case it gets taken away. I've never had customs check my carry on when I come back (beware on smaller flights, sometimes your overhead luggage will go through customs after leaving the plane). I will also take off the labels, so if they ask I'm prepared to say it's just food flavoring, or nicless juice. Had a few bottles in my last flights checked luggage with labels off and nothing happened.
As for flying and in the airport, I am too much a coward to vape out in the open. On flight I will vape in the bathroom once or twice, making sure the steam is gone by the time I go out. Usually it only leaves a slight hint of what your vaping in the air, for all anyone knows it could be perfume. In the airport I use the bathrooms and try to blow it down, as the steam tends to stay in the area you blow it before dispersing.
I know of no airports that have vape only areas, but there are a few airports with sealed off smoking lounges, where if you can smoke cigarettes you can vape. If I have time I will leave the secure area and just go outside, but when I only have a little time between connecting flights I make frequent bathroom stops

One other thing to keep in mind is claim ignorance if you're caught. Smoking laws are in place for combustible tobacco. That means the law only covers burning things and inhaling smoke, not vaping. So while it may be mostly superficial, people seeing vapor and thinking it's smoke, it's best to be polite and do it out of eyes view but there is nothing illegal about it. That all said, airplanes and airports have the right to refuse you service if they catch you.