As someone else mentioned:
With a neoprene neck seal you need to fold the top about 1/2" down the inside on your neck. When you tilt your head forward ask your buddy to look at your neck and make sure it's not gaping. If it is, then you need pull up the torso of your suit so that the back of neck seal isn't being pulled downward.
Another good idea is to make sure your hood fits over the neck seal. If it doesn't then as you move your head, you will encourage water to come trickling into your suit.
There are many schools of thought about using your DS as a BCD. Many of us have tried both approaches and many of us decided to use our BCD for the purpose that it was made for. Since you are a new diver, your instructor is trying not to task load you. As you become comfortable with the basic diving skills that you are learning, you may likely find that your buoyancy is much more easily and precisely controlled by using your BCD. Ultimately try both methods and see which is best for your style of diving.