It is interesting what you posted regarding simplifying English, but you must surely be joking. That is exactly how I felt when traditional Chinese became simplified Chinese, it was very hard to read the characters. Not only were most characters simplified, but some were totally replaced by totally different, albeit homophonic characters. I needed a dictionary ( yes, there are dictionaries for Sim plified to Traditional Chinese) to read those new characters.
Although there are many dialects, it is true that the written language is in simplified or traditional format. However, in the Cantonese dialect, which is spoken in Kuantong, a southern province, and in Hong Kong , they have different words that are not found in the regular Chinese language, and so they have "created" their own characters. I once was given a Hong Kong magazine, and even though I could read it, I could not make sense of what was being read. So, to make it short, being able to recognize the character, may not mean what you think it conveys . Oftentimes they also use a western word (because there is no chinese equivalent) and just transcribe it into characters that sound like that word. Foreign names are mostly transcribed that way. However, I have come across words like "apartment" and "fans" that are also given characters that sound like the western word, but the characters themselves do not mean them. Confusing, right?
As to the original poster, the translations you have posted are adequate to convey the message you need to tell others. There are different ways of saying your phrase, but they all say you will need to go to the hospital if you eat corn. Better to add cornstarch because that is a commonly used thickener, more so than corn, and more unidentifiable
Corn is not commonly used in Chinese dishes. However, there may be occasional use of young babycorn as a vegetable. Not all Chinese cooks use cornstarch as a thickening agent in sauces. Tapioca flour, potato flour, or arrowroot flour can also be used. In America cornstarch is more widely available, and cheaper, so it is most commonly used. In Asia, it might be more common to use tapioca flour, so you may be lucky enough and be able to avoid contact with cornstarch in sauces. However, another caution is there may be cornstarch in fried foods with starchy coatings, like tempura. Anything deep fried and crunchy, or coated, you must ask if there is cornstarch.
One last thing. I don't know if your list would include corn syrup? I am not sure if Chinese bakeries use that ingredient, but it could be a cheap substitute for sugar. You might want to add that to your list.
I hope this helps a bit. Hope you have a good trip and hope you enjoy the food.