Emma gave birth in jail–it was posted in the Storybrooke Mirror. 🙂 And Regina told Emma in the first episode that Henry was 3 weeks old when she adopted him, so it is safe to be sure that Emma gave Henry up for adoption while she was in jail. 🙂
Also, I agree that Emma loved Neil, and I think she still does. She not only kept the car, but made the keychain he gave her into a necklace, and she seems to truly love and miss him, though I am sure she also has resentment towards him as well, of course.