If not, then how is it that he remembers 1000 years of being a centurion?
(“He has a name but the people of our world know him better. As The Last Centurion” - Amy Pond)
If yes, then how has he fathered a child?
He's not plastic. After the Doctor flew the Pandorica into the Sun/TARDIS that rebooted the universe. So that restored Rory to being human. However, due to... timey-wimey, he, Amy, River, and the Doctor still remember the TARDIS exploding and ending the universe, along with the 2000-year wait.
As he is human, I think we all understand how he fathered a child.
Rory got rewritten to a non-automaton version. Although not directly addressed, the reasoning behind this is that when the Doctor flew the Pandorica into the exploding TARDIS to form a universe-wide restoration field (gobbledy-gook from the episode) everything that happened due to the cracks was reversed.
Basically the universe gets rewound to a point before the cracks, at which point Rory had been (and always had been) alive in a non-automaton form. This reversal was shown by Amy's parents re-appearing because, as the Doctor points out, they must have been stolen by the cracks.
As far as I can tell, they don't explain why Amy remembering the Doctor causes him to reappear.