Sometimes they bubble, sometimes they don't. It's not entirely clear why either way.
As for feeding, this is a tricky topic. Photosynthesis provides the vast majority of what they need in terms of energy, but by definition cannot supply protein or vitamins, which are used for growth and various cellular functions. But even a pristine tank will have some dissolved proteins and nutrients that anemones may be able to absorb from the water column. If you are going to feed it to be sure, don't feed it often. Maybe once every week or two, and not a lot.
If a clown hosts the anemone (zero guarantee on that happening) then the clown will feed the anemone through either true symbiosis, sloppy eating habits, or pooping in it.
Just remember, if an organism has a mouth, it must eat something from time to time, even if it's extremely rare.