Well, once Odo did demonstrate the illusion of drinking coffee, so as to fit into a restaurant setting, so it suggests he cannot digest food.
Not really. We know for a fact that he could at least appear to eat actual food - since changelings can hold in blood, they can also hold in food and release it later. Since he doesn't do that, either, one could just as easily deduce that he doesn't want to bother with it all.
Another thing I'd suggest is there is probably a clear difference physiologically between Odo's normal form and a skilled changeling impersonating a human (or klingon, vulcan, whatever). Odo's form may not be really based on anything - it could just be a form he found useful for interacting with humanoids. So if that form lacks the capability to digest things, it may simply be because Odo can't be bothered to form a digestive system. After all - he isn't trying to hide his nature from medical scans.