Is this sentence -- “what china will be like in ten years?”--right or wrong?
This would commonly be considered an incorrect sentence, but the reason has nothing to do with what you are asking about in the rest of this question. I recommend researching word order in interrogative clauses.
Can the phrase “be like” be used with the preposition “in” ?
Yes. There is no particular restriction on this collocation.
when it refers to “after a period of time”, the preposition “in” , as far as I know, is usually with a verb.( grammatically called accomplishments) which indicates that an actions must be finished at some point in the future. For example, they built a house in 2 months(but not “ for 2 months”).
The preposition "in" can be used in that way, but it can also be used in many other ways. For example: "Call me in five minutes." The call does not have to be finished within five minutes.
In this sentence, the action of “build” can not continues endlessly. On the other way, since the phase of “be like” is a state that will last continuously, can it be used with “in” ?
As I noted above, there is no particular restriction on using "be like" with "in".
who can tell me what's the difference of “ for” and “in” when they refer to a period of time?
You should be able to research this on your own. Many dictionaries describe how these words are used when they refer to a period of time, and there are also many grammar websites that give useful descriptions and examples. If you have a specific question about how these words are used (for example, if a dictionary explanation is unclear or if a sentence in a book doesn't seem to follow the rules), then this site would be a good place to ask about that.
and which kind of verbs do they usually use with? Is “be like” usually used with “for”?
The prepositions "for" and "in" can be used with practically any kind of verb. There is no particular restriction on using "be like" with "for".
