Answers to those questions I gave is pretty easily found with a simple Google search. As for the others, do you want answers from an American (me) or a Japanese?
Is English language important in everyday life of a common Japanese citizen? (in a couple of words, explain why)
Only moderately so, but it depends on what line of work they are in, or what their traveling interests/habits are. Many are fascinated with English movies or music (like in karaoke). Japanese language borrows a lot from English and other languages. Watch J TV and you'll see a lot of it slipping into variety and game show chatter.
Where can you get in contact with the English language in Japan? (name couple of fields)
Fields? Science, engineering, medicine, teaching, international business, tourism. All pretty obvious.
What role does the English language fulfill in your country?
"My country" is the U.S. If you mean Japan (where I've lived for the past 14 years), the answer is a combination of the first two answers. International business and scientific research depend heavily on English. They are probably the biggest areas that need it.
Do you think that popularity of the English language can threaten cultural heritage of your country? Why?
No, it does not threaten Japanese cultural heritage. All cultures change daily, if only slowly. The Japanese maintain a strong sense of cultural identity, perhaps too strong. It will never die, and certainly not because of popularity of any language. In fact, without English, Japan's economy will suffer even worse than it is now.
Do you think that the English language will remain popular? Or can it be substituted by other language?
Yes.
Only the dominant one(s) in business and science.