Can constipation cause menstrual like cramps/pain in lower abdomen right below belly button?

Correct. Pain in the lower abdominal can have many causes, such as constipation or diarrhea or gas, bladder infection, menstrual related cramping of your uterus, etc. If your pain persists or worsens, have your doctor examine you. Take care!
Yes, for sure. This may help. Drink at least 2 quarts of water - perhaps warm or hot - until you are past this. Then at least 1-1/2 a day. Eat fruits, veggies, fiber-foods, prunes on a regular basis. Perhaps a mild stool softener or laxative but not past 2 weeks. If still not clear, see your doctor. Try to exercise regularly & be active - never delay when you have the urge to move your bowels. Try a heat pad.