Suppose a researcher uses the application of another researcher's idea in his domain. Given that original researcher knows basics of his idea better, he may help correct any mistakes and give valuable suggestions. In this way, the quality of research paper will be increased. But at the same time, giving away one's complete unpublished paper to unknown person is a matter of a bit worry. In your opinion, should he ask for suggestion or not? If yes, what is a proper way?
It is perfectly acceptable to email your paper to another researcher, and ask if they have any comments or suggestions.
It would also be perfectly acceptable for him to not reply. If he does, the reply might be something short like "Thanks for sending, looks like a nice piece of work!"
If you do write, I'd recommend you do the following:
Keep your email brief and to the point.
Do not ask him to check your paper for mistakes. That's your job. If you feel that you can't do this on your own, then I'd suggest that you offer to make your paper a collaboration with him.
Don't try to be indirect, or hope that he reads between the lines. If you would like to ask him to do something, then it's good manners to do so plainly and directly.
You might also search for and read the many "Why isn't so-and-so responding to my emails" questions which (with good answers) can be found on this site.