Midnight potty runs

[jimnmoe]

Hi! We need help. Rescued a 18month old mini-schnauzer who's whole life has been in kennel for breeding purposes. He is very, very shy and afraid of men or sudden movements.
Problem 1: he will not go for walks. shakes and lays down.
Problem 2: He's great about letting us know he has to go out to do his duty. However, between 1-3 A.M. every night he has to go out and do his duty.
Can anyone suggest a way to change this habit. Lack of sleep is getting to us.
HELP