“Is there a science behind, and do you have (a) particular person (people), that you say the “Shalom Aleichem” to?”
No science, to whoever the three closest available people are.
“Is a minyan preferable?”
Yes.
“Can you ask a woman?”
No.
“must you ask of a Jew?”
Yes.
“Do you need to say “Aleichem Shalom” along with the “friend” that answered you back?”
Our minhag is to do that.
“Did anyone ever refuse to answer your “Shalom Aleichem”?” “
Yes. He was in middle of the bracha.
If so, how did you react?”
I asked someone else. Another time I waited for him to finish the bracha.