Are there any foods that toddlers can't eat or shouldn't eat because of the possibility of allergies?

No. For every study suggesting that a food should be delayed, there's another showing that there is no reason to delay it. At the most recent world allergy congress where all of these data worldwide were presented, the consensus is that there is no consensus; the only reliable recommendation that could be made is that food allergy is less likely to develop in infants who are breastfed for 6-9 months.
no. Recommendations have changed from several years ago. Never give honey to a child less than 1 year. If your toddler has been doing fine with foods so far, there's no need to avoid anything else. It's a good idea to indroduce foods one at a time and watch for any problems - pay attention to foods that have reputation for allergies: peanut, seafood, millk, egg. Avoid choking hazards like popcorn.
Not Sure. The "old" thinking was that delaying introduction of certain common allergens such as peanut butter was beneficial. However newer research suggests the opposite. I think we need more definition and advice from experts.
Let me help. Although honey seems like a wholesome and natural food to give your infant, don't do it until after she's at least 12 months old. Honey can contain spores of a bacterium called clostridium botulinum, which can germinate in a baby's immature digestive system and cause infant botulism, a rare but potentially fatal illness.