You're off by an order of magnitude.

Stars are often trillions of miles apart. Binaries can be so close they touch or as far apart as 100 billion miles.

As for the aliens, there are good arguments for and against their existence. The numerical argument is not, by itself, very convincing. It's like thinking you will win the lotto because you have a million tickets, but not knowing how many balls are drawn and how many numbers are on the balls. You may be guaranteed to win, or your odds may be effectively zero.