It's important the area's to be tested are clean and dry. Food, grease, moisture etc. can affect the number.
That one is a new one on me! Maybe someone else has noticed this. I alternate hands, because my fingers get sore, but I haven't noticed an measurable difference. Have you asked your doctor?
That's a considerable difference if you are testing each hand within a few minutes. I would start by checking my meter and calibrating it (usually by using a 'standard solution' instead of your blood). Could it be possible you're not getting enough blood for a sample from one hand... thicker skin or trouble lancing with your non-dominant hand? You could also try testing the same hand a few times in a row to see if your blood sugar (or your meter's readings) are going up and down that quickly. I would also test with another meter, or have your doc (or nurse) check it and see how it compares to your readings. Good luck!