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Is it okay to ask a woman "So tell me something about yourself" after you've opened the set? If it is or it isn't, please explain the psychology behind it.
After opening... No. Tell stories and be a fun guy that the group will want to keep around. Ignore your target and wait for the attraction to start to build between you and her.
THEN you should start to qualify her... I wouldn't phrase it the way you did however. Using the word "So" to start a sentence shows that you are trying to continue a dying conversation. If a girl does this to you, it shows that she is interested in you.
I say "Tell me 3 interesting things about you that would make me want to get to know you from a hole in the wall" (By telling her to give you 3 things about her, she will not sit there and say "well, what do you want to know?" or have her ummming and awwwing.
If she is attracted to you, she will answer you and begin to qualify herself. If not, neg her and begin building attraction again.