Can an ISP know your search terms?

In a way yes, your ISP has proxy servers - caching one, that save pages of sites visited by their clients, this way other clients within your ISP can access it more quickly. Example, you search myLot in google, if nothing yet at the your proxy, results will be downloaded directly form google, if another client search that already before then what you will get is not from google itself but from your proxy.

Hope this help.

in common, ISP always monitor their network, so they will know what their user do. many country implement this to prevent cyber crime, terrorism,etc

Yes, then can. Since they provide you with your internet access, they receive your search queries, forward them to Google, receive Google's response, and forward that back to you. While they can see everything you do online, it's all automated, so it's likely that no one's looking over your shoulder unless they've seen suspicious activity on your end.

No the search engine doesn;t keep the record.Don't worry.If it does it needs a major hard disc storage as millions of people are searching for different things.And we can sue them for violating our privacy.

Ok, I don't have a professional answer for this, but I would say that with computers ... anything is possible. I watch loads of Law & Order, and if it's anywhere near reality anybody can find out anything that you do on your own pc:)