I'm on a different continent from my siblings both physically and in lifestyle. You've done well to escape the negative influences of your family although it's a shame when families fall apart.
As for chewing gum, you can have anything you like but you cannot fool your body that you're fasting if you're taking in anything but water. As Chrisb1 is often saying (//www.curezone.org/forums/fm.asp?i=1921440#i), any nutrient intake moves you from fasting mode to starvation mode and defeats the object.
"COFFEE AND Sugar FREE GUM WILL BREAK THE FAST, AS YOU ARE SUPPLYING EXTERNAL NOURISHMENT/CALORIES AND SO ON.
SUGAR FREE GUM USUALLY CONTAINS ASPARTAME, A KNOWN CARCINOGEN.
BASICALLY IF YOU CONSUME ANYTHING OTHER THAN WATER, YOU ARE ESSENTIALLY LIVING FROM A STARVATION DIET, WHICH WILL DEPLETE YOUR NUTRITIONAL STORES THAT MORE RAPIDLY, AND PRODUCE DEFICIENCY DISEASES SUCH AS SCURVY AND GENERAL MALNUTRITION.