hey,呢 has two definitions --added to the end of a sentence to make a question which needs a specific answer.(他有什么不喜欢吃的呢？can be interpreted "dose he have anything to dislike to eat..and the answer should be like ..他不喜欢吃鸡肉、土豆（oh,he dosen't like eating chicken 、potato..).Usually can be replaced by 吗（ma）他有什么不喜欢吃的呢？or 他有什么不喜欢吃的吗，they are equal to each other....Usually,when these guys appear ,you should know it is a question.(你在做什么呢？what are you doing ? ---你在吃饭了吗？have you eaten..) but sometimes 呢 can be used to emphasize what you are saying..他有什么不喜欢吃的呢？also means :he has no excuse to dislike the food served to him..(妈妈那么辛苦地给他做了晚饭，他有什么不喜欢吃的呢？Mom worked so hard to make his dinner,there is no way that he will dislike to eat)..in this situation ,the question dose not expect a direct answer exept :yeah ,right.. so ,it is really hard to understand a individual sentence without knowing the whole backgroud.. by the way,it is great to answer your question.it is helpful for me to understand my own language well.wish you good luck with your homework..

他有什么不喜欢吃的呢=what doesn't him like to eat? If the sentence is a rhetorical question, and it means:he like to eat anything.

this sentence means the talker has a query for there is anything he doesn't like. it means the talker thinks that he likes eating everything.

我们不认为用英语能解释清楚。

About learning 虚词/function word/Chinese particle, I recommend 《现代汉语八百词(增订本)》for reference, a most useful grammar book/dictionary by 吕叔湘/Lv Shuxiang, a linguist of Chinese. You can find your answers in the book. Unfortunately, it's wholly written in Chinese. http://resources.allsetlearning.com/chinese/grammar/%E7%8E%B0%E4%BB%A3%E6%B1%89%E8%AF%AD%E5%85%AB%E7%99%BE%E8%AF%8D%EF%BC%88%E5%A2%9E%E8%AE%A2%E6%9C%AC%EF%BC%89 http://www.amazon.cn/%E7%8E%B0%E4%BB%A3%E6%B1%89%E8%AF%AD%E5%85%AB%E7%99%BE%E8%AF%8D/dp/B001198GSW/ref=sr_1_1?ie=UTF8&qid;=1345693275&sr;=8-1 http://www.amazon.cn/gp/switch-language/product/B001198GSW?ie=UTF8&language;=en_CN&qid;=1345693275&sr;=8-1