- What kind/kinds of food and drinks can I have in China?
- My favorite food is egg/the egg?
For the 2 sentences above, which words would you choose?
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Your alternatives are correct, they just mean different things
"Kinds of food" asks for multiple kinds. "Kind of food" asks of one "kind". You would probably ask "What kind of food" since you are only really looking for an example, not a long list of many kinds of food in China.
Saying "kind of food and drinks" would be understood as "kind of food and kind of drinks".
It's not a very useful question, given how large China is. And its not clear what is a "kind of food".
Similarly the word "the" carries meaning. "The egg" refers to a particular egg or egg based food that both the speaker and hearer can identify:
I tried egg noodles and rice noodles. My favourite was the egg.
But normally you are talking about egg in general, and here it is being used to mean the uncountable food type. You could also use a plural
He likes chicken, but my favourite food is egg. I love eggs!
Both "egg" and "the egg" are rather unusual in this context, since "egg" is a rather plain food, it is not often a favourite.