The meaning is clear, but it could be better phrased : "When I start a new conversation with someone, I (always) want to get an idea about who I'm talking to, i.e. his or her age, gender, etc.".

"When I start a conversation with someone new, I always want to gain some general information about the person I am talking to/with: their age, gender and such" seems more suitable. If you don't know whether a person is male or female, use the pronoun "they". Also, 'approximate insight' seems like a literal translation. However, the meaning of the original sentence is clear.

I don't think you need to use the word "approximate" here. If you just say "I want to gain some insight" that already means just some idea and not full knowledge. Or you could say, "Whenever I start a conversation with someone new, I always want to get some idea of who I'm talking to, like their age, gender, and such." In everyday/informal English you can say "their" instead of "his or her".