2nd person vs 3rd person are they interchangeble?

Question

Hi everyone! I am trying to understand the difference between the 3rd person and the 2nd person. It seems to me that they are interchangeable when you are having a direct conversion with someone. One is formal and other is informal?

For example:
Quiere monstrarme el problema'(formal')
vs
Quieres monstrarme el problema'(informal')

How about asking a girl to dance?

quieres bailar'(if I've met this girl before)
vs
quiere bailar'( if I've never met her before)

So when i talk to strangers, I should talk to them in 3rd person right?
Thank you for your help.

Duy