The one-year molars could definitely be the problem. Children's Motrin at bedtime (check with your pediatrician for the correct dose) should help.
As far as eating, kids' diets are drastically reduced after they turn one. Their growth slows down a lot, so they don't need as much. Plus, they're very busy exploring their world and just don't have time to eat!
About the "picky" part, you've just entered the realm of toddler food battles. If he refuses to eat something, don't try to offer alternatives "just so he'll eat something." He'll soon learn that he can get what he wants if he holds out long enough or fusses enough. Simply take his refusal to eat (or playing in his food, or throwing it down, etc.) as a cue that he's not that hungry. Remove him from the table and don't waste your time trying to convince him to eat. Just serve him something nutritious at the next meal or snack time (toddlers generally eat 3 meals, morning snack, afternoon snack, and sometimes bedtime snack -- he will have plenty of opportunities to eat, so don't fret!)
Also, a portion size for a kid his age is literally a couple of tablespoons of something. For example, one quarter of a peanut-butter and jelly sandwich and a couple slices of apple will make a meal for him. He's getting enough to eat, but it doesn't look like it because there's not much gone from his plate.
Keep reminding yourself that he won't starve himself. If he misses a meal or two, you can bet he'll make up for it at the next one. Mine (ages 2 and 4) have each had times where they went a full day where I'm not sure they ate more than a couple bites of cereal and a handful of grapes. However, the next day they ate whatever I put in front of them, and asked for seconds!
Also, try not to let him drink his calories. My daughter went through a no-eating phase for a while as a toddler before I realized she was drinking tons of milk at each meal. Her tummy was full of milk, so of course she wasn't hungry for dinner. As soon as we started monitoring (and limiting) her milk intake, she started eating better.