You draw only one card, no matter how many permanents were put into your hand from the battlefield during that turn.

The permanent that was returned to your hand doesn't have to still be there.

If a token is returned to your hand, it's put there before it ceases to exist.

Barrin's last ability checks the entire turn, even before Barrin was on the battlefield.

If a permanent wasn't put into your hand from the battlefield before your end step begins, Barrin's ability doesn't trigger at all.