Proxy baptisms don't convert anybody. Baptism is merely an ordinance that is required in the event that the person decides to convert.
To allow them to join the Church, yes. To force them to join the Church, no.
Yes, everyone will get the chance to choose for themselves. That doesn't mean that everyone will make the same choice. Billions will likely not choose to convert. That choice will not consign them to outer darkness.
True, you didn't give a number or a percentage, but you did say that those who did not convert to Mormonism would end up in outer darkness, which is absolutely false.
That's false, too, but to go into any detail on this point would take us even further off topic than we already are. In brief, "exaltation in the Celestial Kingdom" requires certain things that are not needed just to get into the Celestial Kingdom.
I realize that, but you need to recognize that your understanding is incomplete. That's why I stepped in to make the corrections I did.