P.M.
Your son is entering an extremely normal phase. He's probably not growing fast right now, and his appetite will wane until he starts a new growth spurt. Meanwhile, his tummy only holds about ONE TABLESPOON of food per meal per year. Many of his needed calories are still coming from formula and milk.
His taste buds have also become extremely sensitive – scientists believe this is a natural development in humans that helps prevent toddlers from poisoning themselves (we didn't always have preservatives and refrigerators, and many plants are toxic). He has fallen back on a few 'safe' foods that he likes and digests well. This can be an excruciatingly long stage for parents, but most kids emerge by four, at the latest, and begin eating a wider range of foods again. A multivitamin for the next few years is probably a good idea.
You'll do well to NOT introduce him to high-fat, high-sugar, and artificially-enhanced foods right now. It will be tempting, but those foods can actually reduce his interest in natural, healthy foods, and you'll stuggle with the consequences for years. Do give him tiny tastes of a variety of foods. Some he will eventually accept, some he'll keep rejecting until he comes through this phase. He can't help that – he can't make himself like foods that disgust him.
And the throwing, ah, yes. That's a developmental stage of its own, though it usually coordinates 'nicely' with high chairs and rejected foods. But almost all children go through the overhand throwing stage (and this often includes overhand hitting with hands or long toys), which is making important eye-hand-spatial-timing connections in your little guy's brain and body. He'll probably do it a lot for the coming year. It's a developmental 'compulsion,' like crawling or walking. Give him plenty of throwing practice during play periods to help him with the needed brain connections.
Deal with it as a practical reality, and ideally with a touch of humor and creativity. I've known parents who put a tarp under the high chair at mealtime. Or let the dog clean up afterward. Or put a few soft toys on the high chair tray, and a box or basket for the child to use for target practice. Try giving him only one or two bites of food at a time, and recognize that he'll be full much sooner that your brain is okay with.
Many littles do well grazing through the day. It's much easier to get a bite or two of fruit, omelet, toast and peanut butter, or a smoothie into a child who's happy and active and feeling momentarily peckish than a restless baby writhing and throwing at the table.
You can let him down to play when he stops eating and starts throwing. He'll learn table manners as he becomes able – I know quite a few kids who's parents gradually expected more and more of them as table companions, and by the time they're 4 or 5, they are at least as civilized as kids who've been forced to sit at table from infancy.