Everything you write suggests that you are just not ready to be on anything steeper than the small hill you describe.
Your anxiety stems from your inexperience. I distinctly remember having that same fear years ago, but I quickly attributed it to the fact that I could not link turns and control my speed at such a steep pitch.
Once I improved, my confidence grew and the fear went away( on that hill). I still look down and get anxious, but its on steeper terrain than before. Get it?
As for the lift, I feel anxious nearly everytime I get on one. I have a fear of heights. I have found that riding the lift with a friend, or even talking to some random on the chair with me helps.
As said before too, do not look out too far. I focus down or on someone or my gear. I always hang on too, even when there is a ski bar.