残念ながら、他の方の回答は間違いです。 これは　許可／不許可　のpermitを聞く時に　親しい友人間で使います。 あり（ありえる）／なし（ありえない）　=　positive／negative I'm sorry that other answers are wrong. I think It's a kind of slang. These words are used in order to ask a permission to friends. So I'll trancerate your example to English. "Can I order (or bring or buy) my favorite food?" Can you understand what I want to say?

好きな食べものあり This sentence is grammatically wrong. It must be 好きな食べものある or 好きな食べものあります. If my guess is correct, the "ari" u mean is a very colloquial way of saying that something is an option. For example, u and ur friends are talking about what u want to have for dinner. 1. U can say 魚はどう？ And ur friend may answer by saying あり, which means that fish is an option and your friend may consider eating fish for dinner. 2. Or u can ask 魚はあり？ This is almost the same meaning as 1. when u say "how about fish?"

this sentence means "what foods you like to eat ?" i think あり is colloquial and abridged of ありますか？also ある is very often in colloquial speak. hope to see native speaker's answer.

Used in us. Told it ment thank you , short american gratitude

Could you give some context? Show how it looks in the sentence you found the word in. There are many words that are read as "ari" and each of them have a different meaning. You can only tell the meaning through context of spoken word or in writing when the Kanji is given.