1) Your female is always pregnant before you put her in the hut. Keep dropping your male on the female till you see your population count go up, then drop him on her again, and she will have the baby. No need for the hut.

2) Sometimes the baby takes a minute or two to show up, depending on how many villagers you have, and how much you have going on at once.

3) When the counter reaches 0, it takes 1 minute for them to drop the baby. Wait, and they will drop it, or go do something for a few minutes and come back. they will drop it eventually.