No, it will not pass the smog test with a defective or removed O2 sensor.
There are many symptoms of a bad O2 sensor. Some are poor fuel efficiency, flashing check engine light, the failure to pass a smog test, and rough idling.
If the vehicle has excessive miles it may be burning oil, If you are sure it is in OK condition to pass the test, Try this, drive the vehicle at highway speed for atleast 10 miles, this will get the emissions system up to full operating condition, and make it reduce smog at its max.
Providing that the vehicle does not have to pass an emissions test
Yes
You can't.
It has to be repaired. A recent reset is an auto fail. You can't have any resets in last 100 miles, but it is easy and cheap to replace
You have more than one O2 sensor in that vehicle and they are all threaded into the exhaust at various points.
The O2 sensor on a Honda Prelude is found on the exhaust pipes of the vehicle. They are located near the catalytic converter which is place on the underside of the chassis.
Start at the exhaust manifold and follow the exhaust pipe toward the rear of the vehicle and you will find the O2 sensor.
The O2 sensor on a 2000 Hyundai Elantra is removed by disconnecting the wiring harness and unscrewing the sensor from its housing. It can then be removed from the vehicle, inspected, and replaced if needed.
There is more than one O2 sensor on that vehicle and they are all threaded into the exhaust system at various points.
Oxygen Sensor Circuit (Rich Exhaust). This may of may not be a defective O2 sensor. It may be something else that is effecting the O2 sensor. But considering the vehicle is 22 years old, I would suspect the O2 sensor needs replacing. I would replace the O2 sensor.