P0422 means your catalyst is inefficient. If both your oxygen sensors are
working properly, you'll need a new catalytic converter. Be sure to check
for any exhaust leaks. If your front pipe or manifold is leaking, the
oxygen sensors can't work properly.
P1123 indicates your PCM is delivering significantly less fuel than it
thinks the engine should need based on the input from the oxygen sensors,
the mass air flow sensor, the crankshaft sensor (engine speed) and the
throttle position sensor. This could be due to an injector leaking into
the cylinder, excessive fuel pressure, anything which would cause the fuel
to go unburned in the combustion chamber (misfire), or a misreading sensor.
This is likely the toughest of your problems to isolate.
P1703 represents the transmission computer believing the throttle position
sensor is out of specification.
Your car was made around the time Hyundai was having some throttle
position sensor issues. I'd start by replacing the throttle position
sensor. It can be affecting your transmission operation, but based on
your descriptions, I hesitate to express confidence it will repair all
your transmission problems. You could be looking at a major transmission
repair. If this fixes your transmission issues, I'd then look for an
exhaust leak and repair any leaks found. If there are none, you'll need
to address the P1123 issue and figure out whether your oxygen sensors are
working properly. If so, you'll need a new catalytic converter (based on
P0422). If I recall correctly, the main catalytic converter on your car
is part of the exhaust manifold. In any event, if you're replacing a
converter, you'll need to replace the one between the two oxygen sensors.