If you use vegetable oils and you see any smoke or charring, depending on the exact oil you'll likely ingest some nasty compounds. (There is quite a bit of research on the air quality, related to restaurant kitchen environments and such, indicating the smoke and vapors are quite bad for you. Lots of carcinogenic compounds in particular.)
Funnily enough, lard is likely healthier than vegetable oil in this respect.
With air convection ovens, the chemical changes are much smaller than when frying on a pan, because the temperature is better controlled. I do my air fries at 180-200'C, and a sprinkling of (seasoned) canola or sunflower oil gives a very nice crispy surface texture without becoming hot enough to produce any unwanted compounds (that occurs only near and above the smoke point). It is too hot for olive oil, though, which starts to smoke at about 190'C.
(I warmly recommend Santa Maria Potato Seasoning Mix for air-fried potatoes. Yummy.)
For my burgers on a skillet, I use 1:5 chopped bacon to low fat beef mince mix for ~ 130g patties. These require no oil on a non-stick pan. I take care to not overheat the non-stick pan, and use wooden (birch) spatula for flipping.