I had surgery to remove a mass out of my chest in 2005, I can still feel my sternum move and pop. Is this normal?

No it is not. Since it has been so long since your operation most likely your bone has healed by non union, which means that there is scar tissue there but the bone has not come together and healed properly. Rarely this can be due to chronic infection. Either way you need to see your surgeon. He or she will determine the extent of the problem and discuss treatment options, risks and benefits .
No. Sounds like sternal non-union, meaning the sternum did not completely heal. The patient should see a board certified thoracic surgeon.
No. You probably have non-reunion sternum, meaning your sternum longitudinally split at the time of the surgery has not reunited. If you feel disabled by this condition, it can be fixed by a surgical procedure.