Should I be concerned about belly pain and bleeding at two months?

Yes. Bleeding in the first trimester suggests possible miscarriage. It can also be due to other causes. Cramping and bleeding together are worrisome. In all cases it is best for women to contact their OB providers for an evaluation and diagnosis.
Yes. You will worry until you know that the pregnancy is okay. You should probably see your doctor for an ultrasound or some blood tests.
Yes. Chronic belly pain can be lots of severe diseases. Bleeding by the mouth or from the rectum is never normal. See your regular doc asap.
Yes. Severe belly pain and heavy bleeding would indicate a possible miscarriage. You should see your doctor.