How to send a mail to a person here? I really don't know where can I find information about it. It can help to solve my problem Prove the polynomial ring and algebra of quaternions isomorphisms.
I have received one email from math.SE (it is not hard to find my email). It was someone demanding to know why I voted to close a question. I did not respond. I would respond to most emails, given that the emails are written in good faith and worth my time.
To answer your question of "how to send mail" - the answer is that if someone has their email on their profile
(or it is easily findable) and your email is written in good faith and not a waste of their time, then you may send an email. In all other cases don't. There is no private messaging feature (other than maybe creating a chat) for a reason.
This is a question and answer site, not a discussion forum. Rarely should you have a need to email someone and even more rarely is it worth their time.