Well my advice to you is:
It is going to take some time to get comfortable with admits. The best thing you can do is watch other nurses admit and get as much experience with admits as possible. First try to get experience with the less critical babies so you can find your own routine when admitting a baby and as you get quicker then you can move on to more critical babies. Admissions can be very stressful and I used to hate them, but now they don't bother me much unless it is an hour before the end of my shift
As far as education goes that will take time as well. Eric hit it right on. The best way to get a basic understanding of disease process is to read handouts designed for families/lay people. March of Dimes has a great web site with lots of easy to understand info. on neonatal disease processes. I suggest you go there and read.
Right now you are still very new and most likely task oriented as most new nurses are. It's very hard to see the "big picture" That will take a long time. Right now you are just focused on what you have to get done in your shift and hoping that you do it right. I can remember when I was a new grad still in orientation and my preceptor said that our intubated baby needed suctioning, but we could wait until we got back from lunch. I was so focused and nervous about suctioning that baby so during lunch that was all I could think about. Now suctioning an intubated baby is no big deal at all, but as a new nurse it freaked my out.
As you gain more experience and confidence then you won't be so task oriented and you will get a firm grasp on the "big picture" with your patients.
Remember to be patient with yourself. It will take at least a year or two to feel comfortable in the NICU environment, but even after years of experience there will still be situations that come up that you are uncomfortable with.
Good luck and keep us updated! Sounds like you are doing a good job!