Wouldn't a echocardiogram show early heart failure? Also wouldn't a stethoscope and chest X-ray show copd?

No... An echocardiogram will not show the fluid in the lungs so it will not diagnose early heart failure. Copd, by definition, has chronic airways obstruction which is diagnosed via pulmonary function testing. This is the only way to differentiate COPD from asthma, both of which can give the same stethoscope and x-ray findings.
Not 100% An echo would tend to have abnormalities in heart failure. It is very sensitive in detecting if the pumping action is decreased. (systolic failure). Still 50% of patients have a kind of heart failure called "diastolic failure, here the heart fails to "relax" properly. This can be detected via echo but is more difficult. Neither xray nor exam is very sensitive for copd, both can be normal in copd.
Not necessarily. An ekg may be entirely normal in early heart failure. Pulmonary function tests are necessary to identify COPD and rate it's severity. While a stethoscope and chest xray may give information about the lungs, they are relatively insensitive when diagnosing copd.