Can I determine if I am a diabetic by using a glucose monitor?

Its possible. There's a few different diagnostic criteria for diagnosing diabetes. The simplest one, is any random blood sugar greater than 200. The other criteria involve checking 2 separate fasting levels, or taking a glucose tolerance test or checking your blood for something called an a1c.
Yes. A morning fasting value of greater than 126 will indicated diabetes as well as any random blood sugar of 200 or more. Both of these readings should be repeated on another day to verify. This should be done with guidance from your physician.