Is it normal for a patient to request stress testing, ecg, echo, and other tests twice in a year if the patient gets more cardiac symptoms after test?

No: You have a test performed to confirm a suspected diagnosis. Tests should not be done as a fishing expedition to see let's see now what we can find now. And tests always have to be interpreted within a margin of error. They are not perfect. They are guideposts to help a doctor in thinking about what may be going on with his patient. What the patient tells the doc is the key!